InterviewSolution
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InterviewSolution
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If `(3 sin theta + 5 cos theta ) = 5, ` prove that ` (5 sin theta - 3 cos theta ) = pm 3. ` |
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Answer» We have `(3 sin theta + 5 cos theta)^(2) + (5 sin theta - 3 cos theta)^(2) ` ` = 9 (sin^(2) theta + cos^(2) theta ) + 25 ( sin^(2) theta + cos^(2) theta) ` ` = (9+ 25)= 34.` ` therefore (3 sin theta + 5 cos theta)^(2) + ( 5 sin theta - 3 cos theta)^(2) =34 ` ` rArr 5^(2) + (5 sin theta - 3 cos theta)^(2) = 34 " " [ because 3 sin theta + 5 cos theta = 5 ] ` ` rArr (5 sin theta - 3 cos theta) = pm 3 " " `[ taking square root on each side] Hence, `(5 sin theta - 3 cos theta) = pm 3. ` |
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