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TRIGONOMETRIC FUNCTIONS — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSTRIGONOMETRIC FUNCTIONS2 Marks
Question
Prove that: ${\sin ^2}\frac{\pi }{6} + {\cos ^2}\frac{\pi }{3} - {\tan ^2}\frac{\pi }{4} = - \frac{1}{2}$
✓

Answer

We have
L.H.S. $ = {\sin ^2}\frac{\pi }{6} + {\cos ^2}\frac{\pi }{3} - {\tan ^2}\frac{\pi }{4}$
$ = {\left( {\frac{1}{2}} \right)^2} + {\left( {\frac{1}{2}} \right)^2} - {(1)^2}$$ = \frac{{1 + 1 - 4}}{4} = \frac{{ - 2}}{4}$
$ = \frac{{ - 1}}{2}$ RHS

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