If Tan X = a B , Show that a Sin X − B Cos X a Sin X + B Cos X = a 2 − B 2 a 2 + B 2

Question

If \[\tan x = \frac{a}{b},\] show that

\[\frac{a \sin x - b \cos x}{a \sin x + b \cos x} = \frac{a^2 - b^2}{a^2 + b^2}\]

Solution

LHS:
\[\frac{a\sin x - b\cos x}{a\sin x + b\cos x}\]
Dividing by \[b\cos x: \]
\[ = \frac{\frac{a\tan x}{b} - 1}{\frac{a\tan x}{b} + 1}\]
Substituting the value of \[\tan x\]
\[ = \frac{a^2 - b^2}{a^2 + b^2}\]
= RHS
Hence proved.

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Trigonometric Equations

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Q 20 Q 19 Q 21

Chapter 5: Trigonometric Functions - Exercise 5.1 [Page 18]

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R.D. Sharma Mathematics [English] Class 11

Chapter 5 Trigonometric Functions
Exercise 5.1 | Q 20 | Page 18

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