Advertisements
Advertisements
प्रश्न
Prove that sin(π + θ) = − sin θ.
Advertisements
उत्तर
L.H.S = sin(π + θ)
= sin π cos θ + cos π sin θ
= (0) cos θ + (– 1) sin θ
= – sin θ
= R.H.S
APPEARS IN
संबंधित प्रश्न
Find the values of cot(660°)
Find the values of `tan ((19pi)/3)`
Find the values of `sin (-(11pi)/3)`
Find all the angles between 0° and 360° which satisfy the equation sin2θ = `3/4`
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)
Find sin(x – y), given that sin x = `8/17` with 0 < x < `pi/2`, and cos y = `- 24/25`, x < y < `(3pi)/2`
If a cos(x + y) = b cos(x − y), show that (a + b) tan x = (a − b) cot y
Show that cos2 A + cos2 B – 2 cos A cos B cos(A + B) = sin2(A + B)
Prove that cot(A + B) = `(cot "A" cot "B" - 1)/(cot "A" + cot "B")`
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)`
If θ is an acute angle, then find `sin (pi/4 - theta/2)`, when sin θ = `1/25`
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 4x + sin 2x)/(cos 4x + cos 2x)` = tan 3x
Show that cot(A + 15°) – tan(A – 15°) = `(4cos2"A")/(1 + 2 sin2"A")`
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 sin2 B + sin2 C = 1
Choose the correct alternative:
`1/(cos 80^circ) - sqrt(3)/(sin 80^circ)` =
Choose the correct alternative:
`(1 + cos pi/8) (1 + cos (3pi)/8) (1 + cos (5pi)/8) (1 + cos (7pi)/8)` =
