Trigonometric Functions of Sum and Difference of Angles

1. For any two angles A and B, cos (A -B) = cos A cos B + sin A sin B

2. For any two angles A and B, cos (A + B) = cos A cos B − sin A sin B

3. For any two angles A and B, sin (A − B) = sin A cos B − cos A sin B

4. For any two angles A and B, sin (A + B) = sin A cos B + cos A sin B

5. For any two angles A and B, tan (A + B) =` (tan A + tan B)/(1 –tan A tan B)`

6. For any two angles A and B, tan (A -B) = `(tan A -tan B)/(1 + tan A tan B)`

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Prove the following:

`(cos(x - y))/(cos(x + y)) = (cotx coty + 1)/(cotx coty - 1)`

Prove the following:

`sqrt(2)cos (pi/4 - "A")` = cos A + sin A

Prove the following:

`((1 + tan x)/(1 - tan x))^2 = tan(pi/4 + x)/(tan(pi/4 - x))`

If sin A = `(-5)/13, pi < "A" < (3pi)/2` and cos B = `3/5, (3pi)/2 < "B" < 2pi` find sin (A + B)

If sin A = `(-5)/13, pi < "A" < (3pi)/2` and cos B = `3/5, (3pi)/2 < "B" < 2pi` find cos (A – B)

If sin A = `(-5)/13, pi < "A" < (3pi)/2` and cos B = `3/5, (3pi)/2 < "B" < 2pi` find tan (A + B)

Select the correct option from the given alternatives :

If tan A – tan B = x and cot B – cot A = y, then cot (A – B) = _____

Select the correct option from the given alternatives :

The value of `costheta/(1 + sin theta)` is equal to ……