Advertisements
Advertisements
Question
If θ is an acute angle, then find `sin (pi/4 - theta/2)`, when sin θ = `1/25`
Advertisements
Solution
`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
RELATED QUESTIONS
Find the values of `sin (-(11pi)/3)`
Find the value of the trigonometric functions for the following:
cos θ = `- 2/3`, θ lies in the IV quadrant
Find the value of the trigonometric functions for the following:
tan θ = −2, θ lies in the II quadrant
Find all the angles between 0° and 360° which satisfy the equation sin2θ = `3/4`
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)
Find the value of cos 105°.
Prove that cos(30° + x) = `(sqrt(3) cos x - sin x)/2`
If a cos(x + y) = b cos(x − y), show that (a + b) tan x = (a − b) cot y
If x cos θ = `y cos (theta + (2pi)/3) = z cos (theta + (4pi)/3)`. find the value of xy + yz + zx
If θ is an acute angle, then find `cos (pi/4 + theta/2)`, when sin θ = `8/9`
Prove that (1 + sec 2θ)(1 + sec 4θ) ... (1 + sec 2nθ) = tan 2nθ
Express the following as a sum or difference
sin 4x cos 2x
Express the following as a product
cos 35° – cos 75°
Prove that 1 + cos 2x + cos 4x + cos 6x = 4 cos x cos 2x cos 3x
Prove that cos(30° – A) cos(30° + A) + cos(45° – A) cos(45° + A) = `cos 2"A" + 1/4`
Show that cot(A + 15°) – tan(A – 15°) = `(4cos2"A")/(1 + 2 sin2"A")`
If A + B + C = 2s, then prove that sin(s – A) sin(s – B)+ sin s sin(s – C) = sin A sin B
