Advertisements
Advertisements
प्रश्न
Express the following as a sum or difference
2 sin 10θ cos 2θ
Advertisements
उत्तर
2 sin 10θ cos 2θ
We know
2 sin A cos B = sin(A + B) + sin(A – B)
Take A = 10θ, B = 2θ
2 sin 10θ . cos 2θ = sin(10θ + 2θ) + sin(10θ – 2θ)
2 sin 10θ . cos 2θ = sin 12 θ + sin 8θ
2 sin 10θ . cos 2θ = `1/2`[sin 12θ + sin 8θ]
APPEARS IN
संबंधित प्रश्न
Find the values of `tan ((19pi)/3)`
Find the value of the trigonometric functions for the following:
cos θ = `2/3`, θ lies in the I quadrant
If sin x = `15/17` and cos y = `12/13, 0 < x < pi/2, 0 < y < pi/2` find the value of sin(x + y)
Find the value of sin105°.
Find the value of tan `(7pi)/12`
Prove that cos(π + θ) = − cos θ
Expand cos(A + B + C). Hence prove that cos A cos B cos C = sin A sin B cos C + sin B sin C cos A + sin C sin A cos B, if A + B + C = `pi/2`
Prove that sin(45° + θ) – sin(45° – θ) = `sqrt(2) sin θ`
Prove that cos 8θ cos 2θ = cos25θ – sin23θ
Find the value of cos 2A, A lies in the first quadrant, when cos A = `15/17`
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 cos A + cos B − cos C = `- 1 + 4cos "A"/2 cos "B"/2 sin "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 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 cos B – cos C = `- 1 + 2sqrt(2) cos "B"/2 sin "C"/2`
Choose the correct alternative:
If cos 28° + sin 28° = k3, then cos 17° is equal to
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
