Advertisements
Advertisements
Question
Show that cos2 A + cos2 B – 2 cos A cos B cos(A + B) = sin2(A + B)
Advertisements
Solution
L.H.S = cos2 A + cos2 B – 2 cos A cos B [cos A cos B – sin A sin B]
= cos2 A + cos2 B – 2 cos2 A cos2 B + 2 sin A cos A sin B cos B
= (cos2 A – cos2 A cos2 B) + (cos2 B – cos2 A cos2 B) + 2 sin A cos A sin B cos B
= cos2A(1 – cos2 B) + cos2B(1 – cos2 A) + 2 sin A cos A sin B cos B
= cos2A sin2B + cos2B sin2A + 2 sin A cos B sin B cos A
= (sin A cos B + cos A sin B)2
= sin2 (A + B)
= R.H.S
APPEARS IN
RELATED QUESTIONS
Find the values of cot(660°)
Find the value of the trigonometric functions for the following:
cos θ = `- 1/2`, θ lies in the III quadrant
Find the value of the trigonometric functions for the following:
tan θ = −2, θ lies in the II quadrant
Find sin(x – y), given that sin x = `8/17` with 0 < x < `pi/2`, and cos y = `- 24/25`, x < y < `(3pi)/2`
Find the value of cos 105°.
Prove that sin(45° + θ) – sin(45° – θ) = `sqrt(2) sin θ`
Prove that `tan(pi/4 + theta) tan((3pi)/4 + theta)` = – 1
Find the value of tan(α + β), given that cot α = `1/2`, α ∈ `(pi, (3pi)/2)` and sec β = `- 5/3` β ∈ `(pi/2, pi)`
Find the value of cos 2A, A lies in the first quadrant, when sin A = `4/5`
Prove that cos 5θ = 16 cos5θ – 20 cos3θ + 5 cos θ
Prove that (1 + tan 1°)(1 + tan 2°)(1 + tan 3°) ..... (1 + tan 44°) is a multiple of 4
Show that sin 12° sin 48° sin 54° = `1/8`
Prove that sin x + sin 2x + sin 3x = sin 2x (1 + 2 cos x)
If A + B + C = 180◦, prove that sin 2A + sin 2B + sin 2C = 4 sin A sin B sin C
If A + B + C = 180°, prove that sin(B + C − A) + sin(C + A − B) + sin(A + B − C) = 4 sin A sin B sin C
If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that sin2 B + sin2 C = 1
Choose the correct alternative:
Let fk(x) = `1/"k" [sin^"k" x + cos^"k" x]` where x ∈ R and k ≥ 1. Then f4(x) − f6(x) =
