Question:
Question 10: If 16 cot x = 12, then (sinx - cosx)/(sinx + cosx) equals
Answer:
Given 16 cot x = 12
=> cot x = 12/16
=> cot x = 3/4
Now (sinx - cosx)/(sinx + cosx) = {(sinx - cosx)/sinx}/{(sinx + cosx)/sinx} [divide by sinx in numerator and denominator]
=> (sinx - cosx)/(sinx + cosx) = (sinx/sinx - cosx/sinx)/(sinx/sinx + cosx/sinx)
=> (sinx - cosx)/(sinx + cosx) = (1 - cotx)/(1 + cotx)
=> (sinx - cosx)/(sinx + cosx) = (1 - 3/4)/(1 + 3/4)
=> (sinx - cosx)/(sinx + cosx) = {(4 - 3)/4}/{(4 + 3)/4}
=> (sinx - cosx)/(sinx + cosx) = (1/4)/(7/4)
=> (sinx - cosx)/(sinx + cosx) = 1/7
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