If ( A)/( B)=n, ( A)/( B)=m , then the value of (m^ 2 -n^ 2 ) ^ 2 B is

Correct answer: B. 1- ^ 2 A=n B and A=m B Squaring and adding, we get 1=n^ 2 ^ 2 B+m^ 2 ^ 2 B array ll & 1=n^ 2 (1- ^ 2 B)+m^ 2 ^ 2 B & (m^ 2 -n^ 2 ) ^ 2 B=1-n^ 2 array

BITSAT 2015

Exam: BITSAT
Year: 2015
Subject: Mathematics
Chapter: Trigonometric Ratios & Identities

BITSAT 2015 · Mathematics · Trigonometric Ratios & Identities

If ( A)/( B)=n, ( A)/( B)=m , then the value of (m^ 2 -n^ 2 ) ^ 2 B...

\frac{\cos A}{\cos B}=n, \frac{\sin A}{\sin B}=m

, then the value of \left(m^{2}-n^{2}\right) \sin ^{2} B$ is

Options

A $1+\mathrmn^{2}$
B $1-\mathrmn^{2}$
C $\mathrmn^{2}$
D $-\mathrmn^{2}$

Correct answer

B. $1-\mathrmn^{2}$

Step-by-step solution

\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

\begin{array}{ll} \Rightarrow& 1=n^{2}\left(1-\sin ^{2} B\right)+m^{2} \sin ^{2} B \\ \therefore & \left(m^{2}-n^{2}\right) \sin ^{2} B=1-n^{2} \end{array}

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