Question

Prove that: (sin α + cosec α)2 + (cos α + sec α)2 = (7 + tan2α + cot2α).

for class 10​

Answer 1

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We need to prove (sinα+cosecα)² +(cosα+secα)² =k² +tan² α+cot² α

Taking LHS =sin ²α+cosec² α+2+cos² α+sec² α+2

=5+1+tan² α+1+cot² α

=7+cot² α+tan² α

Therefore, k² =7

Answer 2

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We need to prove (sinα+cosecα)² +(cosα+secα)² =k² +tan² α+cot² α

Taking LHS =sin ²α+cosec² α+2+cos² α+sec² α+2

=5+1+tan² α+1+cot² α

=7+cot² α+tan² α

Therefore, k² =7