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The sum of all possible solution of trigonometric equation `2sqrt(cos^(6)theta-sin^(6)theta)=cos2theta+1` in interval `[pi,7pi]` is equal toA. `7pi`B. `14pi`C. `28pi`D. `42pi` |
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Answer» Correct Answer - A Given, `2sqrt(cos^(6)theta-sin^(6)theta)=cos2theta+1` `4(cos^(6)theta-sin^(6)theta)=(cos2theta+1)^(2)implies4((1+cos2theta)/(2))^(3)-4((1-cos2theta)/(2))^(3)=(1+cos2theta)^(2)` `implies" "(1+cos2theta)^(3)-(1-cos2theta)^(3)=2[1+2cos2theta+cos^(2)2theta]` `implies" "2(cos^(3)2theta+3cos2theta)=(1+2cos2theta+cos^(2)2theta)` `implies" "cos^(3)2theta-cos^(2)2theta+cos2theta-1=0` `implies" "(cos2theta-1)(cos^(2)2theta+1)=0` `:." "cos2theta=1" "implies" "2theta=2npi` `" "theta=npi," "ninI` Sum of al solution `=pi+2pi+3pi+.........+7pi` `=pi(1+2+3+.........+7)` `=pi((7)(8))/(2)=28pi` |
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