Advertisements
Advertisements
Question
Prove that sin(π + θ) = − sin θ.
Advertisements
Solution
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
RELATED QUESTIONS
Find the values of sin(480°)
Find all the angles between 0° and 360° which satisfy the equation sin2θ = `3/4`
Show that `sin^2 pi/18 + sin^2 pi/9 + sin^2 (7pi)/18 + sin^2 (4pi)/9` = 2
Prove that cos(30° + x) = `(sqrt(3) cos x - sin x)/2`
Prove that sin(30° + θ) + cos(60° + θ) = cos θ
Prove that sin 105° + cos 105° = cos 45°
Prove that `tan(pi/4 + theta) tan((3pi)/4 + theta)` = – 1
Find the value of cos 2A, A lies in the first quadrant, when cos A = `15/17`
Find the value of cos 2A, A lies in the first quadrant, when sin A = `4/5`
If A + B = 45°, show that (1 + tan A)(1 + tan B) = 2
Express the following as a sum or difference
cos 5θ cos 2θ
Express the following as a sum or difference
sin 5θ sin 4θ
Show that sin 12° sin 48° sin 54° = `1/8`
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 A + B + C = `pi/2`, prove the following sin 2A + sin 2B + sin 2C = 4 cos A cos B cos C
If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that cos B – cos C = `- 1 + 2sqrt(2) cos "B"/2 sin "C"/2`
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
