if sin square x + cos square x + tan square x + cot square x + sec square x + cosec square x =7 find the value of sin square x ,cos square x and more

if sin x + cos x - root 2 sin x =0 find the value of tan square x ,cot square x and tan square x + cot square x

3- if x to the power x+y=y cube and y to the power x+ y =x6y3 x and y r natural numbers find x to the power y and y to the power x

Given:

 

Put sin²x = t, we have a quadratic equation–

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