If ( cos A/ cos B) = n, ( sin A / sin B) = m, then the value of (m2 - n2) sin2 B is

Question

If ( cos A/ cos B) = n, ( sin A / sin B) = m, then the value of (m2 - n2) sin2 B is (A) 1 + n2 (B) 1 - n2 (C) n2 (D)  - n2

Tardigrade Admin · Accepted Answer

cos A = n cos B and sin A = m sin B Squaring and adding, we get 1 = n2 cos2 B + m2 sin2 B ⇒ 1 = n2 (1 - sin2 B) + m2 sin2 B ∴ (m2 - n2) sin2 B = 1 - n2

Q. If $\frac{c o s A}{c o s B} = n, \frac{s i n A}{s i n B} = m$ , then the value of $(m^{2} - n^{2}) sin^{2} B$ is

$1 + n^{2}$

$1 - n^{2}$

$n^{2}$

$- n^{2}$

$cos A = n cos B$ and $sin A = m sin B$
Squaring and adding, we get
$1 = n^{2} cos^{2} B + m^{2} sin^{2} B$
$\Rightarrow 1 = n^{2} (1 - sin^{2} B) + m^{2} sin^{2} B$
$∴ (m^{2} - n^{2}) sin^{2} B = 1 - n^{2}$

Q. If cosBcosA​=n,sinBsinA​=m, then the value of (m2−n2)sin2B is

1+n2

1−n2

n2

−n2