Question

Answer this please.......................

Answer 1

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Answer 2

Question:

[ [ sec²(90-theta) - cot²theta ] / [ 2( sin²25 + sin²65) ]  ] + [2cos²60 / (sin30 + cos60) ]

Answer:

[ [ sec²(90-theta) - cot²theta ] / [ 2( sin²25 + sin²65) ]  ] + [2cos²60 / (sin30 + cos60) ]

⇒ [ ( cosec² theta - cot² theta ) / 2 (cos²65 + sin²65) ] + [2cos²60 / (sin30 + cos60) ]      [ because sec²(90-theta) = cosec² theta ]

⇒ 1 / ( 2*1 ) + [2 * cos²60 / (sin30 + cos60) ]  [ we know that cosec² theta - cot² theta = 1 and cos²theta  + sin²theta = 1  ]

⇒ 1/2 + [ (2 * 1/4) / (1/2 + 1/2) ]  [ we also know that cos60 = 1/2 and sin30 = 1/2 ]

⇒ 1/2 + 1/2

⇒ 1

So, the final answer is 1.