Advertisements
Advertisements
प्रश्न
If θ is an acute angle, then find `cos (pi/4 + theta/2)`, when sin θ = `8/9`
Advertisements
उत्तर
`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
संबंधित प्रश्न
Find the values of tan(1050°)
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
Show that `sin^2 pi/18 + sin^2 pi/9 + sin^2 (7pi)/18 + sin^2 (4pi)/9` = 2
Find the value of tan `(7pi)/12`
If a cos(x + y) = b cos(x − y), show that (a + b) tan x = (a − b) cot y
Show that tan(45° − A) = `(1 - tan "A")/(1 + tan "A")`
Find the value of cos 2A, A lies in the first quadrant, when sin A = `4/5`
Find the value of cos 2A, A lies in the first quadrant, when tan A `16/63`
Prove that (1 + tan 1°)(1 + tan 2°)(1 + tan 3°) ..... (1 + tan 44°) is a multiple of 4
Show that `cot(7 1^circ/2) = sqrt(2) + sqrt(3) + sqrt(4) + sqrt(6)`
Express the following as a sum or difference
2 sin 10θ cos 2θ
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`
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 `tan "A"/2 tan "B"/2 + tan "B"/2 tan "C"/2 + tan "C"/2 tan "A"/2` = 1
If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that cos2 B + cos2 C = 1
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)` =
Choose the correct alternative:
`(sin("A" - "B"))/(cos"A" cos"B") + (sin("B" - "C"))/(cos"B" cos"C") + (sin("C" - "A"))/(cos"C" cos"A")` is
