A) 9
B) 7
C) 5
D) 3
Correct Answer: B
Solution :
\[{{(\sin \alpha +cosec\alpha )}^{2}}+{{(\cos \alpha +\sec \alpha )}^{2}}\] \[=k+{{\tan }^{2}}\alpha +{{\cot }^{2}}\alpha \] L.H.S. \[{{\sin }^{2}}\alpha +\cos e{{c}^{2}}\alpha ++2\sin \alpha \,\cos ec\alpha +{{\cos }^{2}}\alpha +\]\[{{\sec }^{2}}\alpha +2\cos \alpha \sec \alpha \] \[=1+\cos e{{c}^{2}}\alpha +2+2+{{\sec }^{2}}\alpha \] \[=1+1+{{\cot }^{2}}\alpha +2+2+1+{{\tan }^{2}}\alpha \] \[=7\,{{\cot }^{2}}\alpha +{{\tan }^{2}}\alpha \] On comparing with R.H.S, we get\[k=7\].
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