Trigonometric Functions · Class 11 · CBSE · Science Mathematics
For all real values of x for which the expressions are defined, prove that (1 − cos x)/sin x = sin x/(1 + cos x).
Practice question from Trigonometric Functions (Class 11 · CBSE · Science Mathematics), with the correct answer and a step-by-step solution.
medium · Subjective · Q-437BEA
For all real values of x for which the expressions are defined, prove that (1 − cos x)/sin x = sin x/(1 + cos x).
Answer: Starting with the left-hand side, multiply the numerator and denominator by 1 + cos x: [(1 − cos x)(1 + cos x)]/[sin x(1 + cos x)] = [1 − cos²x]/[sin x(1 + cos x)]. Using 1 − cos²x = sin²x, this becomes sin²x/[sin x(1 + cos x)] = sin x/(1 + cos x), which is the right-hand side.
Solution
Rationalise the left-hand side by multiplying by . Then use and cancel the common factor , which is permitted because the expressions are assumed to be defined.
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