Advertisements
Advertisements
Question
Prove that `(cot(180^circ + theta) sin(90^circ - theta) cos(- theta))/(sin(270^circ + theta) tan(- theta) "cosec"(360^circ + theta))` = cos2θ cotθ
Advertisements
Solution
`(cot(180^circ + theta) sin(90^circ - theta) * cos(- theta))/(sin(270^circ + theta) tan(- theta) "cosec"(360^circ + theta))`
= `(cot theta* costheta costheta)/(- cos theta xx - tantheta xx "cosec" theta)`
= `(cot theta * cos^2theta)/(cos theta tan theta "cosec" theta)`
= `(cot theta * cos^2theta)/(cos theta * sintheta/costheta * 1/sin theta)`
= `cos^2theta * cottheta`
APPEARS IN
RELATED QUESTIONS
Prove that cos(π + θ) = − cos θ
Prove that sin(30° + θ) + cos(60° + θ) = cos θ
If a cos(x + y) = b cos(x − y), show that (a + b) tan x = (a − b) cot y
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
If cos(α – β) + cos(β – γ) + cos(γ – α) = `- 3/2`, then prove that cos α + cos β + cos γ = sin α + sin β + sin γ = 0
Show that tan(45° + A) = `(1 + tan"A")/(1 - tan"A")`
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 cos θ = `1/2 ("a" + 1/"a")`, show that cos 3θ = `1/2 ("a"^3 + 1/"a"^3)`
Prove that (1 + sec 2θ)(1 + sec 4θ) ... (1 + sec 2nθ) = tan 2nθ
Express the following as a sum or difference
2 sin 10θ cos 2θ
Express the following as a sum or difference
cos 5θ cos 2θ
Express the following as a sum or difference
sin 5θ sin 4θ
Express the following as a product
sin 50° + sin 40°
Prove that `(sin x + sin 3x + sin 5x + sin 7x)/(cos x + cos x + cos 5x cos 7x)` = tan 4x
If A + B + C = 180°, prove that sin2A + sin2B − sin2C = 2 sin A sin B cos C
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 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 A + B + C = `pi/2`, prove the following cos 2A + cos 2B + cos 2C = 1 + 4 sin A sin B sin C
