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Erpress the following as sum or difference of trigonometric ratios 2sin 6 degree × sin 66degree |
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Answer» Consider the equation,Case 1- 2sin4θcos2θ sinA+sinB=2SIN( 2A+B )COS( 2A−B ) =2sin( 26θ+2θ )cos( 26θ−2θ ) =2sin4θcos2θCase 2- 2sin2θcos4θ sinA+sinB=2sin( 2A+B )cos( 2A−B ) =2cos( 26θ+2θ )SIN( 26θ−2θ )Case 3- 2sin2θsin4θ cosA−cosB=−2sin( 2A+B )sin( 2A−B ) =−2sin( 26θ+4θ )sin( 26θ−2θ ) =2sin2θsin4θ Case 4-2cos2θcos4θ cosA−cosB=2cos( 2A+B )cos( 2A−B ) =2cos( 26θ+4θ )cos( 26θ−4θ ) =2cos2θcos4θHence, PROVED. |
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