Cos A Cos B Formula

Trigonometry is a co-operative of mathematics that studies the relationships between angles and lengths of triangles. It is a very important topic of mathematics just similar statistics, linear algebra and calculus. In addition to mathematics, it also contributes majorly to engineering, physics, astronomy and architectural design. Trigonometry Formulas for class 11 play a crucial function in solving any trouble related to this chapter. Also, check Trigonometry For Class eleven where students tin learn notes, as per the CBSE syllabus and prepare for the test.
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Trigonometry Formulas For Grade 11 – PDF

Listing of Class 11 Trigonometry Formulas

Here is the list of formulas for Class 11 students every bit per the NCERT curriculum. All the formulas of trigonometry chapter are provided hither for students to help them solve problems speedily.

Trigonometry Formulas

sin(−θ) = −sin θ

cos(−θ) = cos θ

tan ( − θ ) = − tan θ

c o south e c ( − θ ) = − c o due south eastward c θ

sec ( − θ ) = sec θ

cot ( − θ ) = − cot θ

Production to Sum Formulas

sin x sin y = ane/ii [cos(x–y) − cos(10+y)]

cos x cos y = 1/ii[cos(x–y) + cos(ten+y)]

sin 10 cos y = 1/ two [ sin ( x + y ) + sin ( x − y ) ]

cos x sin y = 1/ 2 [ sin ( x + y ) – sin ( x − y ) ]

Sum to Product Formulas

sin x + sin y = 2 sin [(x+y)/2] cos [(x-y)/two]

sin x – sin y = 2 cos [(x+y)/2] sin [(x-y)/2]

cos x + cos y = ii cos [(x+y)/2] cos [(x-y)/2]

cos x – cos y = -2 sin [(x+y)/2] sin [(ten-y)/two]

Identities

sin^two A + cosⁱⁱ A = ane

1+tan² A = sec² A

1+cot² A = cosec² A

Sign of Trigonometric Functions in Different Quadrants

Quadrants→	I	II	3	4
Sin A	+	+	–	–
Cos A	+	–	–	+
Tan A	+	–	+	–
Cot A	+	–	+	–
Sec A	+	–	–	+
Cosec A	+	+	–	–

Bones Trigonometric Formulas for Grade eleven

cos (A + B) = cos A cos B – sin A sin B

cos (A – B) = cos A cos B + sin A sin B

sin (A+B) = sin A cos B + cos A sin B

sin (A -B) = sin A cos B – cos A sin B

Based on the to a higher place addition formulas for sin and cos, we become the post-obit below formulas:

sin(π/2-A) = cos A
cos(π/2-A) = sin A
sin(π-A) = sin A
cos(π-A) = -cos A
sin(π+A)=-sin A
cos(π+A)=-cos A
sin(2π-A) = -sin A
cos(2π-A) = cos A

If none of the angles A, B and (A ± B) is an odd multiple of π/2, and so

tan ( A + B ) = [(tan A + tan B)/( one – tan A tan B)]
tan ( A- B ) = [(tan A – tan B)/( 1 + tan A tan B)]

If none of the angles A, B and (A ± B) is a multiple of π, then

c o t ( A + B ) = [(c o t A c o t B − 1)/(c o t B + c o t A)]
c o t ( A- B ) = [(c o t A c o t B + 1)/(c o t B – c o t A)]

Some additional formulas for sum and product of angles:

cos(A+B) cos(A–B)=cos²A–sin²B=cos²B–sinⁱⁱA
sin(A+B) sin(A–B) = sinⁱⁱA–sin^twoB=cos²B–cos^twoA
sinA+sinB = 2 sin (A+B)/2 cos (A-B)/2

Formulas for twice of the angles:

sin2A = 2sinA cosA = [2tan A /(1+tanⁱⁱA)]
cos2A = cosⁱⁱA–sinⁱⁱA = 1–2sinⁱⁱA = 2cos^twoA–ane= [(i-tan²A)/(1+tanⁱⁱA)]
tan 2A = (2 tan A)/(1-tan²A)

Formulas for thrice of the angles:

sin3A = 3sinA – 4sin^threeA
cos3A = 4cosⁱⁱⁱA – 3cosA
tan3A = [3tanA–tan³A]/[1−3tan²A]

Video Lesson on Trigonometry

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Trigonometry Formulas
Trigonometry Formulas Listing
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Solved Examples

Example 1:

If sin 𝜃 = –4/five and 𝜋 < 𝜃 < iii𝜋/2, discover the value of all the other five trigonometric functions.

Solution:

Since, the value of theta ranges betwixt 𝜋 < 𝜃 < 3𝜋/2, that ways, 𝜃 lies in third quadrant.

Now, sin 𝜃 = –⅘ ⇒ cosec 𝜃 = 1/sin 𝜃 = – v/4

∴ cot ² 𝜃 = (cosec ² 𝜃 – 1) = (25/sixteen – 1) = 9/16 ⇒ cot 𝜃 = ¾ (taking positive root as cot 𝜃 is positive in third quadrant)

tan 𝜃 = 1/cot 𝜃 = iv/iii

Now, cos 𝜃 = cot 𝜃 sin 𝜃 = ¾ × (– ⅘ ) = – ⅗

∴ sec 𝜃 = 1/cos 𝜃 = – v/iii

Hence, all other trigonometric functions are cos 𝜃 = – ⅗, tan 𝜃 = four/3, cot 𝜃 = ¾, sec 𝜃 = – 5/3 and cosec 𝜃 = – 5/4.

Example two:

Evaluate: cos( – 870 ^o )

Solution:

cos( – 870 ^o ) = cos(870 ^o ) [as cos ( –𝜃) = cos 𝜃 ]

= cos ( 2 × 360 ^o + 150 ^o )

= cos 150 ^o [as cos (2n𝜋 + 𝜃) = cos 𝜃 ]

= cos ( 180 ^o – thirty ^o ) = – cos 30 ^o = – √3/2

Example iii:

Prove that tan 56 ^o = (cos xi ^o + sin 11 ^o )/(cos 11 ^o – sin 11 ^o )

Solution:

We have, LHS tan 65 ^o = tan (45 ^o + 11 ^o )

= (tan 45 ^o + tan 11 ^o )/(ane – tan 45 ^o tan 11 ^o ) {since, 45 ^o + xi ^o is non an odd multiple of 𝜋/2 }

= (one + tan 11 ^o )/(1 – tan 11 ^o )

= {1 + (sin 11 ^o /cos 11 ^o )}/ {1 – (sin eleven ^o /cos eleven ^o )}

= (cos 11 ^o + sin 11 ^o )/(cos 11 ^o – sin 11 ^o ) = RHS

Case 4:

Prove that sin x + sin 3x + sin 5x + sin 7x = 4sin 4x cox 2x cos x.

Solution:

Now, LHS = (sin 7x + sin x) + (sin 5x + sin 3x)

= ii sin {(7x + x)/2} cos {(7x – x)/2} + 2 sin {(5x + 3x)/2} cos {(5x – 3x)/2}

= 2 sin 4x cos 3x + 2 sin 4x cos ten

= 2 sin 4x (cos 3x + cos x)

= 2 sin 4x × 2 cos {(3x + x)/2} cos {(3x – x)/ii}

= 2 sin 4x × 2 cos 2x cos x

= iv sin 4x cos 2x cos x = RHS

Practise Problems

Prove that (sin ten – sin y)/(cos x + cos y) = tan {(x – y)/2}.
Prove that sin 𝜋/ten + sin thirteen𝜋/10 = – ½.
Prove that (one + cos 𝜃)/(ane – cos 𝜃) = (cosec 𝜃 + cot 𝜃) ^two
If A + B + C = 𝜋, prove that sin 2A + sin 2B + sin 2C = iv sin A sin B sin C.

Frequently Asked Questions on Trigonometry Formulas For Class 11

What are the topics in trigonometry class 11?

The following are covered in CBSE Class 11 trigonometry:
Angles: Positive and Negative
System of Measuring angles: Sexagesimal (Degree Measure) and Circular System (Radian Mensurate); the relationship between both the systems
Trigonometric Functions (sine, cosine, tangent, co-tangent, secant, co-secant)
Trigonometric Identities
Sign of trigonometric functions in various quadrants
Values of some special angles of trigonometric functions
Trigonometric functions as sum and difference of angles
Trigonometric functions of multiples angles
Conditional identities
Trigonometric Equations
Sine formula, cosine formula, Napier's Analogies

What are the three basic identities of trigonometric functions?

The three ground trigonometric identities are
sin² 10 + cosⁱⁱ ten = 1
1 + tan^two x = sec² x
cosec² ten = 1 + cot^two x

What are the signs of the trigonometric functions in various quadrants?

In the 1st quadrant, all trigonometric ratios are positive, in the 2nd quadrant, merely sine and cosecant are positive, in the 3rd quadrant, tangent and co-tangent are positive, and in the fourth quadrant, merely cosine and secant are positive.

What is the value of tan 3x?

Tan 3x = [iii tan x – tan^three ten]/[1 − 3 tan² 10]