If 10 sin⁴a + 15cos⁴a =6, find the value of 27cosec⁶a + 8sec⁶a

Dear Ankit ,

 convert cos⁴a =( 1 sin²a)²

 sunstitue in eq and u will get a quadratic eq. ,    25sin⁴a - 30sin²a + 9 =0

so sina = sqrt. (3/5)

now cosec a = sqrt. ( 5/3 )

seca = sqrt. ( 5/2 )

substitue in 27cosec⁶a + 8sec⁶a and find the value.

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Askiitians Expert

Anil Pannikar

IIT Bombay

we get cos a =sqarerootof 2/5. and then find 'cosec a' and 'sec a'  we get the reqd. one as 250