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Multiple Choice Questions
1. What is the least value of $$tan^2θ + cot^2θ + sin^2θ + cos^2θ + sec^2θ + cosec^2θ$$ ?
(A): 1
(B): 3
(C): 5
(D): 7
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By: anil on 05 May 2019 01.48 am
Expression : $$tan^2θ + cot^2θ + sin^2θ + cos^2θ + sec^2θ + cosec^2θ$$ Using, $$(sec^2 heta-tan^2 heta=1)$$ and $$(cosec^2 heta-cot^2 heta=1)$$ = $$(sin^2 heta+cos^2 heta)+tan^2 heta+cot^2 heta+(1+tan^2 heta)+(1+cot^2 heta)$$ = $$1+1+1+2tan^2 heta+2cot^2 heta$$ = $$3+2(tan^2 heta+cot^2 heta)$$ Minimum value of $$(tan^2 heta+cot^2 heta)=2$$ = $$3+2(2)=3+4=7$$ => Ans - (D)
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2017 SSC CGL 09 Aug Shift-1
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