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Q. 10.tan theta +cot theta = sec theta csc theta

Ans.

start from left side

tan theta + cot theta

convert sines into cosines

write tan theta in sines and cosines using quotient identity

sin theta/cos theta/cot theta

write cot theta in sines and cosines using quotient identity

sin theta/cos theta+cos theta/sin theta

sin theta sin theta+cos theta cos theta/cos theta sin theta

Apply pythagorean identity

1/cos theta csc theta

1/cos theta.1/sin theta

Multiply 1/cos theta and 1/sin theta

1/cos theta sin theta

I hope it will be helpful for you

the revenue of the fitness center, y, is the product of two factors: the number of members and the fee paid by each member. there are 320 members now, but number of members goes down by 10 for each $5 increase in fees, so if x is the number of $5 price increases then members is equal to (320 - 10x). since the fee is currently $45, and the fee increases by $5 for every price bump x, the fee is given by (45 + 5x). so, revenue y is given by y = (320 - 10x)(45 + 5x).

the correct answer would be the third option