Advertisements
Advertisements
प्रश्न
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
उत्तर
`(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
संबंधित प्रश्न
Find the values of tan(1050°)
Find the value of the trigonometric functions for the following:
cos θ = `- 2/3`, θ lies in the IV quadrant
Find all the angles between 0° and 360° which satisfy the equation sin2θ = `3/4`
Find cos(x − y), given that cos x = `- 4/5` with `pi < x < (3pi)/2` and sin y = `- 24/25` with `pi < y < (3pi)/2`
Prove that cos(π + θ) = − cos θ
Prove that sin(π + θ) = − sin θ.
Prove that sin(30° + θ) + cos(60° + θ) = cos θ
Show that tan(45° − A) = `(1 - tan "A")/(1 + tan "A")`
If tan x = `"n"/("n" + 1)` and tan y = `1/(2"n" + 1)`, find tan(x + y)
Find the value of tan(α + β), given that cot α = `1/2`, α ∈ `(pi, (3pi)/2)` and sec β = `- 5/3` β ∈ `(pi/2, pi)`
Prove that `tan (pi/4 + theta) - tan(pi/4 - theta)` = 2 tan 2θ
Express the following as a product
cos 35° – cos 75°
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`
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 = 2s, then prove that sin(s – A) sin(s – B)+ sin s sin(s – C) = sin A sin B
If A + B + C = `pi/2`, prove the following cos 2A + cos 2B + cos 2C = 1 + 4 sin A sin B sin C
If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that cos2 B + cos2 C = 1
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
