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 (-(11pi)/3)`
Find the value of the trigonometric functions for the following:
tan θ = −2, θ lies in the II quadrant
If sin x = `15/17` and cos y = `12/13, 0 < x < pi/2, 0 < y < pi/2` find the value of sin(x + y)
If sin A = `3/5` and cos B = `9/41 0 < "A" < pi/2, 0 < "B" < pi/2`, find the value of sin(A + B)
Prove that cos(30° + x) = `(sqrt(3) cos x - sin x)/2`
Find a quadratic equation whose roots are sin 15° and cos 15°
Prove that sin(n + 1) θ sin(n – 1) θ + cos(n + 1) θ cos(n – 1)θ = cos 2θ, n ∈ Z
Prove that cos(A + B) cos(A – B) = cos2A – sin2B = cos2B – sin2A
Show that tan(45° − A) = `(1 - tan "A")/(1 + tan "A")`
Find the value of cos 2A, A lies in the first quadrant, when cos A = `15/17`
If θ is an acute angle, then find `sin (pi/4 - theta/2)`, when sin θ = `1/25`
If cos θ = `1/2 ("a" + 1/"a")`, show that cos 3θ = `1/2 ("a"^3 + 1/"a"^3)`
Prove that `tan (pi/4 + theta) - tan(pi/4 - theta)` = 2 tan 2θ
Express the following as a sum or difference
sin 4x cos 2x
Show that sin 12° sin 48° sin 54° = `1/8`
Prove that `sin theta/2 sin (7theta)/2 + sin (3theta)/2 sin (11theta)/2` = sin 2θ sin 5θ
Show that cot(A + 15°) – tan(A – 15°) = `(4cos2"A")/(1 + 2 sin2"A")`
If A + B + C = 180°, prove that sin2A + sin2B − sin2C = 2 sin A sin B cos C
If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that sin2 B + sin2 C = 1
Choose the correct alternative:
cos 1° + cos 2° + cos 3° + ... + cos 179° =
