Advertisements
Advertisements
Question
Prove that cos 8θ cos 2θ = cos25θ – sin23θ
Advertisements
Solution
L.H.S = cos 8θ cos 2θ
= cos(5θ + 3θ) cos(5θ – 3θ)
We know cos(A + B) cos(A – B)
= cos2 A – sin2 B
∴ cos(5θ + 3θ) cos(5θ – 3θ) = cos25θ – sin23θ
= R.H.S
APPEARS IN
RELATED QUESTIONS
Find the values of cot(660°)
Find the value of sin105°.
Find the value of tan `(7pi)/12`
Find a quadratic equation whose roots are sin 15° and cos 15°
Prove that cos(A + B) cos C – cos(B + C) cos A = sin B sin(C – A)
Prove that sin2(A + B) – sin2(A – B) = sin2A sin2B
Prove that cot(A + B) = `(cot "A" cot "B" - 1)/(cot "A" + cot "B")`
If tan x = `"n"/("n" + 1)` and tan y = `1/(2"n" + 1)`, find tan(x + y)
Find the value of cos 2A, A lies in the first quadrant, when tan A `16/63`
If θ is an acute angle, then find `cos (pi/4 + theta/2)`, when sin θ = `8/9`
Prove that (1 + tan 1°)(1 + tan 2°)(1 + tan 3°) ..... (1 + tan 44°) is a multiple of 4
Express the following as a sum or difference
cos 5θ cos 2θ
Show that sin 12° sin 48° sin 54° = `1/8`
Show that `(sin 8x cos x - sin 6x cos 3x)/(cos 2x cos x - sin 3x sin 4x)` = tan 2x
Show that cot(A + 15°) – tan(A – 15°) = `(4cos2"A")/(1 + 2 sin2"A")`
If A + B + C = 180°, prove that sin A + sin B + sin C = `4 cos "A"/2 cos "B"/2 cos "C"/2`
If A + B + C = `pi/2`, prove the following cos 2A + cos 2B + cos 2C = 1 + 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:
`1/(cos 80^circ) - sqrt(3)/(sin 80^circ)` =
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) =
