Question

(sin@ + cosec@ )^2 + (cos@+sec@)^2 =7 tan^2@ + cot^2@​

Answer 1

Hope this will help you (^_^)

Answer 2

(cos θ + secθ )² + (sin θ + cosecθ ) ² = 7 + tan ² θ + cot ² θ 

We take RHS 
7 + tan ² θ + cot ² θ 
=5+1+tan ² θ +1+ cot ² θ 

=5+ sec² θ+ cosec ² θ 

=1+2+2+ sec² θ+ cosec ² θ 

=(cos² θ +sin ² θ)+2(cos θ sec θ )+2(sin θ cosec θ )+ 
+sec² θ+ cosec ² θ 

=(cos² θ +2 cos θ sec θ +sec² θ) 
+(sin ² θ+2sin θ cosec θ + cosec ²θ) 

=(cos θ + secθ )² + (sin θ + cosecθ )² 


(PROVED)

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