Advertisements
Advertisements
Question
Find the value of cos 2A, A lies in the first quadrant, when tan A `16/63`
Advertisements
Solution
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
RELATED QUESTIONS
Find the values of cot(660°)
Prove that `(cot(180^circ + theta) sin(90^circ - theta) cos(- theta))/(sin(270^circ + theta) tan(- theta) "cosec"(360^circ + theta))` = cos2θ cotθ
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)
Find sin(x – y), given that sin x = `8/17` with 0 < x < `pi/2`, and cos y = `- 24/25`, x < y < `(3pi)/2`
Find the value of cos 105°.
Find the value of tan `(7pi)/12`
Prove that cos(A + B) cos(A – B) = cos2A – sin2B = cos2B – sin2A
Prove that cot(A + B) = `(cot "A" cot "B" - 1)/(cot "A" + cot "B")`
Find the value of cos 2A, A lies in the first quadrant, when sin A = `4/5`
Prove that (1 + tan 1°)(1 + tan 2°)(1 + tan 3°) ..... (1 + tan 44°) is a multiple of 4
Express the following as a product
cos 65° + cos 15°
Prove that 1 + cos 2x + cos 4x + cos 6x = 4 cos x cos 2x cos 3x
If A + B + C = 180°, prove that sin A + sin B + sin C = `4 cos "A"/2 cos "B"/2 cos "C"/2`
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
If x + y + z = xyz, then prove that `(2x)/(1 - x^2) + (2y)/(1 - y^2) + (2z)/(1 - z^2) = (2x)/(1 - x^2) (2y)/(1 - y^2) (2z)/(1 - z^2)`
If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that sin2 B + sin2 C = 1
