Advertisements
Advertisements
प्रश्न
If θ is an acute angle, then find `sin (pi/4 - theta/2)`, when sin θ = `1/25`
Advertisements
उत्तर
`sin (pi/4 - theta/2)`, when sin θ = `1/25`
`sin (pi/4 - theta/2) = sqrt((1 - cos2(pi/4 - theta/2))/2`
= `sqrt((1 cos(pi/2 - theta))/2`
= `sqrt((1 - sin theta)/2`
= `sqrt((1 - 1/25)/2`
= `sqrt((25 - 1)/50`
= `sqrt(24/50)`
= `sqrt(12/25)`
= `sqrt((4 xx 3)/(5 xx 5)`
= `(2sqrt(3))/5`
APPEARS IN
संबंधित प्रश्न
Find the values of sin(480°)
Find the values of cos(300°)
Prove that `(cot(180^circ + theta) sin(90^circ - theta) cos(- theta))/(sin(270^circ + theta) tan(- theta) "cosec"(360^circ + theta))` = cos2θ cotθ
Find cos(x − y), given that cos x = `- 4/5` with `pi < x < (3pi)/2` and sin y = `- 24/25` with `pi < y < (3pi)/2`
Prove that cos(30° + x) = `(sqrt(3) cos x - sin x)/2`
Prove that cos(π + θ) = − cos θ
Expand cos(A + B + C). Hence prove that cos A cos B cos C = sin A sin B cos C + sin B sin C cos A + sin C sin A cos B, if A + B + C = `pi/2`
Prove that sin(30° + θ) + cos(60° + θ) = cos θ
Prove that sin(n + 1) θ sin(n – 1) θ + cos(n + 1) θ cos(n – 1)θ = cos 2θ, n ∈ Z
If θ + Φ = α and tan θ = k tan Φ, then prove that sin(θ – Φ) = `("k" - 1)/("k" + 1)` sin α
Find the value of cos 2A, A lies in the first quadrant, when cos A = `15/17`
Find the value of cos 2A, A lies in the first quadrant, when tan A `16/63`
Prove that (1 + sec 2θ)(1 + sec 4θ) ... (1 + sec 2nθ) = tan 2nθ
Show that `((cos theta -cos 3theta)(sin 8theta + sin 2theta))/((sin 5theta - sin theta) (cos 4theta - cos 6theta))` = 1
If A + B + C = 180°, prove that sin2A + sin2B − sin2C = 2 sin A sin B cos 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 x + y + z = xyz, then prove that `(2x)/(1 - x^2) + (2y)/(1 - y^2) + (2z)/(1 - z^2) = (2x)/(1 - x^2) (2y)/(1 - y^2) (2z)/(1 - z^2)`
If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that cos B – cos C = `- 1 + 2sqrt(2) cos "B"/2 sin "C"/2`
Choose the correct alternative:
`(1 + cos pi/8) (1 + cos (3pi)/8) (1 + cos (5pi)/8) (1 + cos (7pi)/8)` =
