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Trigonometric Ratios of Common Angles

How many of t...

Question

How many of the following statements are correct?

SinA + sin B = 2 sin cos

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SinA - sin B = 2 sin cos

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cosA + cos B = 2 cos cos

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cosA - cos B = 2 sin sin

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Solution

The correct options are
A
SinA + sin B = 2 sin cos

B
SinA - sin B = 2 sin cos

C
cosA + cos B = 2 cos cos

(1),(2) and (3) are correct

$4^{t h}$ relation is

cos A - cos B = 2 sin $\frac{(A + B)}{2}$ sin $\frac{(B - A)}{2}$

Suggest Corrections

Similar questions

How many of the following relations are correct?

(1)1. Sin(A+B) = sinAcosB + cosAsinB

(2)2. cos(A-B) = CosAcosB - sinAsinB

(1)3. Tan (A-B) = $\frac{t a n A - t a n B}{1 + t a n A t a n B}$

(2)4. Sin(A+B) (sin(A-B) = $c o s^{2} A - c o s^{2} B$

\frac{s i n (A + B) + s i n (A - B)}{c o s (A + B) + c o s (A - B)} = t a n A

\frac{s i n (A - B)}{c o s A c o s B} + \frac{s i n (B - C)}{c o s B c o s C} + \frac{s i n (C - A)}{c o s C c o s A} = 0

\frac{s i n (A - B)}{s i n A s i n B} + \frac{s i n (B - C)}{s i n B s i n C} + \frac{s i n (C - A)}{s i n C s i n A} = 0

s i n^{2} B = s i n^{2} A + s i n^{2} (A - B) - 2 s i n A c o s B s i n (A - B)

c o s^{2} + c o s^{2} B - 2 c o s A c o s B c o s (A + B) = s i n^{2} (A + B)

\frac{t a n (A + B)}{c o t (A - B)} = \frac{t a n^{2} A - t a n^{2} B}{1 - t a n^{2} A t a n^{2} B}

A + B + C = 180^{o}

{sin}^{2} A + {sin}^{2} B - {sin}^{2} C = 2 sin A sin B cos C

{sin}^{2} A + {sin}^{2} B + {sin}^{2} C = 2 (1 + cos A cos B cos C)

△ A B C,

{sin}^{2} A - {sin}^{2} B + {sin}^{2} C

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