Advertisements
Advertisements
प्रश्न
Find the value of cos 2A, A lies in the first quadrant, when tan A `16/63`
उत्तर
cos 2A = `(1 - tan^2"A")/(1 + tan^2"A")`
= `(1 - (16/63)^2)/(1 + (16/63)^2`
= `((63)^2 - (16)^2)/((63)^2 + (16)^2`
= `((63 + 16) (63 - 16))/(3969 + 256)`
= `(79 xx 47)/4225`
= `3713/4225`
APPEARS IN
संबंधित प्रश्न
Find the values of sin(480°)
Find the value of the trigonometric functions for the following:
cos θ = `2/3`, θ lies in the I quadrant
Show that `sin^2 pi/18 + sin^2 pi/9 + sin^2 (7pi)/18 + sin^2 (4pi)/9` = 2
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 cos(A – B)
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 cos(A + B) cos C – cos(B + C) cos A = sin B sin(C – A)
Prove that sin(n + 1) θ sin(n – 1) θ + cos(n + 1) θ cos(n – 1)θ = cos 2θ, n ∈ Z
Prove that sin(A + B) sin(A – B) = sin2A – sin2B
Prove that cos 8θ cos 2θ = cos25θ – sin23θ
Show that cos2 A + cos2 B – 2 cos A cos B cos(A + B) = sin2(A + B)
If θ is an acute angle, then find `cos (pi/4 + theta/2)`, when sin θ = `8/9`
Show that `cos pi/15 cos (2pi)/15 cos (3pi)/15 cos (4pi)/15 cos (5pi)/15 cos (6pi)/15 cos (7pi)/15 = 1/128`
Show that `((cos theta -cos 3theta)(sin 8theta + sin 2theta))/((sin 5theta - sin theta) (cos 4theta - cos 6theta))` = 1
Prove that sin x + sin 2x + sin 3x = sin 2x (1 + 2 cos x)
If A + B + C = 180°, prove that sin2A + sin2B + sin2C = 2 + 2 cos A cos B cos C
If A + B + C = 180°, prove that sin A + sin B + sin C = `4 cos "A"/2 cos "B"/2 cos "C"/2`
Choose the correct alternative:
`(1 + cos pi/8) (1 + cos (3pi)/8) (1 + cos (5pi)/8) (1 + cos (7pi)/8)` =