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Question

(sinA+cosecA)2+(cosA+secA)2=


A

7+tan2A+sec2A

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B

11+tan2A+cot2A

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C

9+tan2A+cot2A

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D

7+tan2A+cot2A

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Solution

The correct option is D

7+tan2A+cot2A


(sinA+cosecA)2+(cosA+secA)2L.H.S=(sinA+cosecA)2+(cosA+secA)2=(sin2A+cosec2A+2sinAcosecA)+(cos2A+sec2A+2cosAsecA)=(sin2A+cos2A)+2sinA(1sinA)+2cosA(1cosA)+1+tan2A+1+cot2A=1+2+2+2+tan2A+cot2A=7+tan2A+cot2A=R.H.S


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