Advertisements
Advertisements
प्रश्न
Prove that `(sin(4"A" - 2"B") + sin(4"B" - 2"A"))/(cos(4"A" - 2"B") + cos(4"B" - 2"A"))` = tan(A + B)
Advertisements
उत्तर
`(sin(4"A" - 2"B") + sin(4"B" - 2"A"))/(cos(4"A" - 2"B") + cos(4"B" - 2"A")) = (sin{(4"A" - 2"B" + 4"B" - 2"A")/2} cos {(4"A" - 2"B" - 4"B" + 2"A")/2})/(cos{(4"A" - 2"B" + 4"B" - 2"A")/2} cos{(4"A" - 2"B" - 4"B" + 2"A")/2})`
= `(sin((2"A" + 2"B")/2) * cos((6"A" - 6"B")/2))/(cos((2"A" + 2"B")/2) * cos((6"A" - 6"B")/2)`
= `(sin("A" + "B"))/(cos("A" + "B"))`
= tan(A + B)
APPEARS IN
संबंधित प्रश्न
`(5/7, (2sqrt(6))/7)` is a point on the terminal side of an angle θ in standard position. Determine the six trigonometric function values of angle θ
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:
cos θ = `- 2/3`, θ lies in the IV quadrant
If sin x = `15/17` and cos y = `12/13, 0 < x < pi/2, 0 < y < pi/2`, find the value of cos(x − y)
Prove that cos(π + θ) = − cos θ
Prove that sin(A + B) sin(A – B) = sin2A – sin2B
Prove that cos(A + B) cos(A – B) = cos2A – sin2B = cos2B – sin2A
If tan x = `"n"/("n" + 1)` and tan y = `1/(2"n" + 1)`, find tan(x + y)
If θ + Φ = α and tan θ = k tan Φ, then prove that sin(θ – Φ) = `("k" - 1)/("k" + 1)` sin α
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
sin 4x cos 2x
Express the following as a sum or difference
cos 5θ cos 2θ
Express the following as a sum or difference
sin 5θ sin 4θ
Show that cot(A + 15°) – tan(A – 15°) = `(4cos2"A")/(1 + 2 sin2"A")`
If A + B + C = 180°, prove that cos A + cos B − cos C = `- 1 + 4cos "A"/2 cos "B"/2 sin "C"/2`
If A + B + C = 180°, prove that sin2A + sin2B + sin2C = 2 + 2 cos A cos B cos C
If A + B + C = 180°, prove that sin2A + sin2B − sin2C = 2 sin A sin B cos C
