Advertisements
Advertisements
Question
If 2 cos (A + B) = 2 sin (A - B) = 1;
find the values of A and B.
Solution
2 cos (A + B) = 1
cos (A + B) = `(1)/(2)`
cos (A+B) = cos 60°
A + B = 60° ........( 1)
2 sin (A – B) = 1
2 sin (A – B) = `(1)/(2)`
A – B = 30° ........(2)
Adding (1) and (2)
A + B + A – B = 60° + 30°
2A = 90°
A = 45°
A + B = 60°
B = 60° – A
B = 60 – 45°
B = 15°
APPEARS IN
RELATED QUESTIONS
If 2 sin x° - 1 = 0 and x° is an acute angle; find:
- sin x°
- x°
- cos x° and tan x°.
If 4 cos2 x° - 1 = 0 and 0 ∠ x° ∠ 90°,
find:(i) x°
(ii) sin2 x° + cos2 x°
(iii) `(1)/(cos^2xx°) – (tan^2 xx°)`
If 4 cos2 x = 3 and x is an acute angle;
find the value of :
(i) x
(ii) cos2 x + cot2 x
(iii) cos 3x (iv) sin 2x
Solve for x : 3 tan2 (2x - 20°) = 1
Evaluate the following: `((1 - cosθ)(1 + cosθ))/((1 - sinθ)(1 + sinθ)` if θ = 30°
Find the value 'x', if:
Evaluate the following: `(sin36°)/(cos54°) + (sec31°)/("cosec"59°)`
Express each of the following in terms of trigonometric ratios of angles between 0° and 45°: sin65° + cot59°
Express each of the following in terms of trigonometric ratios of angles between 0° and 45°: cos72° - cos88°
Express each of the following in terms of trigonometric ratios of angles between 0° and 45°: cosec64° + sec70°
