If sin Q + cos Q = root(2)sin (90 0 - Q ) , determine cot Q and cosec Q.
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sinQ+cosQ=√2sin(90°-Q)
or, sinQ+cosQ=√2cosQ
or, sinQ=√2cosQ-cosQ
or, sinQ=cosQ(√2-1)
or, sinQ/cosQ=√2-1
or, tanQ=√2-1
∴, cotQ=1/tanQ=1/(√2-1)
or, cotQ=(√2+1)/(√2-1)(√2+1)
or, cotQ=(√2+1)/(2-1)
or, cotQ=√2+1
Again, cosec²Q-cot²Q=1
or, cosec²Q=1+cot²Q
or, cosec²Q=1+(√2+1)²
or, cosec²Q=1+2+2√2+1
or, cosec²Q=4+2√2
or, cosecQ=√(4+2√2)
or, cosecQ=√2(2+√2)
or, sinQ+cosQ=√2cosQ
or, sinQ=√2cosQ-cosQ
or, sinQ=cosQ(√2-1)
or, sinQ/cosQ=√2-1
or, tanQ=√2-1
∴, cotQ=1/tanQ=1/(√2-1)
or, cotQ=(√2+1)/(√2-1)(√2+1)
or, cotQ=(√2+1)/(2-1)
or, cotQ=√2+1
Again, cosec²Q-cot²Q=1
or, cosec²Q=1+cot²Q
or, cosec²Q=1+(√2+1)²
or, cosec²Q=1+2+2√2+1
or, cosec²Q=4+2√2
or, cosecQ=√(4+2√2)
or, cosecQ=√2(2+√2)
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