(B) We are given the equation $(a + b)^2 = 4ab \sin^2 \theta$.Since the range of $\sin^2 \theta$ is $[0, 1]$,we must have $\sin^2 \theta = \frac{(a +

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(B) We are given the equation $(a + b)^2 = 4ab \sin^2 \theta$.Since the range of $\sin^2 \theta$ is $[0, 1]$,we must have $\sin^2 \theta = \frac{(a + b)^2}{4ab} \le 1$.This implies $(a + b)^2 \le 4ab$.Rearranging the terms,we get $(a + b)^2 - 4ab \le 0$,which simplifies to $(a - b)^2 \le 0$.Since the square of any real number cannot be negative,the only possibility is $(a - b)^2 = 0$,which means $a = b$.

Class 11 Mathematics Trigonometrical Ratios, Functions and Identities Maximum and minimum values of trigonometrical functions, Conditional trigonometrical identities

Medium

The equation $(a + b)^2 = 4ab \sin^2 \theta$ is possible only when

A
$2a = b$
B
$a = b$
C
$a = 2b$
D
None of these

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Trigonometrical Ratios, Functions and Identities

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Maximum and minimum values of trigonometrical functions, Conditional trigonometrical identities

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The equation $(a + b)^2 = 4ab \sin^2 \theta$ is possible only when

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