Advertisements
Advertisements
प्रश्न
Prove that cos(A + B) cos C – cos(B + C) cos A = sin B sin(C – A)
Advertisements
उत्तर
L.H.S = (cos A cos B – sin A sin B) cos C – (cos B cos C – sin B sin C) cos A
= cos A cos B cos C – sin A sin B cos C – cos A cos B cos C + cos A sin B sin C
= cos A sin B sin C – sin A sin B cos C
= sin B [sin C cos A – cos C sin A]
= sin B [sin (C – A)]
= R.H.S
APPEARS IN
संबंधित प्रश्न
Find the values of sin (– 1110°)
Find the values of tan(1050°)
Find the values of cot(660°)
Find the value of the trigonometric functions for the following:
cos θ = `- 2/3`, θ lies in the IV quadrant
Find the value of the trigonometric functions for the following:
sec θ = `13/5`, θ lies in the IV quadrant
Show that `sin^2 pi/18 + sin^2 pi/9 + sin^2 (7pi)/18 + sin^2 (4pi)/9` = 2
If sin x = `15/17` and cos y = `12/13, 0 < x < pi/2, 0 < y < pi/2`, find the value of tan(x + y)
Find the value of cos 105°.
Find the value of tan `(7pi)/12`
Prove that sin(45° + θ) – sin(45° – θ) = `sqrt(2) sin θ`
Prove that sin(30° + θ) + cos(60° + θ) = cos θ
Prove that cos(A + B) cos(A – B) = cos2A – sin2B = cos2B – sin2A
Show that tan(45° − A) = `(1 - tan "A")/(1 + tan "A")`
If cos θ = `1/2 ("a" + 1/"a")`, show that cos 3θ = `1/2 ("a"^3 + 1/"a"^3)`
Prove that `tan (pi/4 + theta) - tan(pi/4 - theta)` = 2 tan 2θ
Show that `cot(7 1^circ/2) = sqrt(2) + sqrt(3) + sqrt(4) + sqrt(6)`
Express the following as a sum or difference
2 sin 10θ cos 2θ
