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Trigonometry – I — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsTrigonometry – I1 Mark
Question
Prove the following:
$\sin ^2 A \cos ^2 B+\cos ^2 A \sin ^2 B+\cos ^2 A \cos ^2 B+\sin ^2 A \sin ^2 B=1$
✓

Answer

$\text { L.H.S. }=\sin ^2 A \cos ^2 B+\cos ^2 A \sin ^2 B+\cos ^2 A \cos ^2 B+\sin ^2 A \sin ^2 B$
$=\sin ^2 A\left(\cos ^2 B+\sin ^2 B\right)+\cos ^2 A\left(\sin ^2 B+\cos ^2 B\right)$
$=\sin ^2 A(1)+\cos ^2 A(1)$
$=1=\text { R.H.S. }$

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