Advertisements
Advertisements
Question
If θ is an acute angle, then find `cos (pi/4 + theta/2)`, when sin θ = `8/9`
Advertisements
Solution
`cos (pi/4 + theta/2)`, when sin θ = `8/9`
`cos (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 - 8/9)/2`
= `sqrt((9 - 8)/18`
= `sqrt(1/18)`
= `sqrt(1/(9 xx 2))`
= `1/(3sqrt(2))`
APPEARS IN
RELATED QUESTIONS
Find the values of sin(480°)
Find the values of cot(660°)
Find the value of the trigonometric functions for the following:
cos θ = `2/3`, θ lies in the I quadrant
If sin x = `15/17` and cos y = `12/13, 0 < x < pi/2, 0 < y < pi/2`, find the value of tan(x + y)
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 75° – sin 15° = cos 105° + cos 15°
Show that tan 75° + cot 75° = 4
If x cos θ = `y cos (theta + (2pi)/3) = z cos (theta + (4pi)/3)`. find the value of xy + yz + zx
Prove that cos(A + B) cos(A – B) = cos2A – sin2B = cos2B – sin2A
Show that cos2 A + cos2 B – 2 cos A cos B cos(A + B) = sin2(A + B)
Find the value of cos 2A, A lies in the first quadrant, when tan A `16/63`
Prove that `(sin 4x + sin 2x)/(cos 4x + cos 2x)` = tan 3x
Prove that cos(30° – A) cos(30° + A) + cos(45° – A) cos(45° + A) = `cos 2"A" + 1/4`
Prove that `(sin x + sin 3x + sin 5x + sin 7x)/(cos x + cos x + cos 5x cos 7x)` = tan 4x
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)
If A + B + C = 180°, prove that `tan "A"/2 tan "B"/2 + tan "B"/2 tan "C"/2 + tan "C"/2 tan "A"/2` = 1
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
