ExamBro
ExamBro
AP EAMCET · Maths · Trigonometric Ratios & Identities

If \(\sin x \cosh y=\cos \theta\) and \(\cos x \sinh y=\sin \theta\), then \(\sinh ^2 y=\)

  1. A \(\cosh ^2 x\)
  2. B \(\cos ^2 x\)
  3. C \(\sin ^2 x\)
  4. D \(\sinh ^2 x\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\cos ^2 x\)

Step-by-step Solution

Detailed explanation

\(\left(\sin x \cosh y\right)^2 + \left(\cos x \sinh y\right)^2 = \cos^2 \theta + \sin^2 \theta\) \(\sin^2 x \cosh^2 y + \cos^2 x \sinh^2 y = 1\) \(\sin^2 x (1 + \sinh^2 y) + \cos^2 x \sinh^2 y = 1\) \(\sin^2 x + (\sin^2 x + \cos^2 x) \sinh^2 y = 1\) \(\sin^2 x + \sinh^2 y = 1\)…