If sinA + cosA =2^1/2.•sin(90-A), Find cotA and cosecA.

Question

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Answer 1

Trig identity sin(90-A)=cosA; so sinA=cosA(√2-1), tanA=√2-1 (A=π/8 or 22.5º.)

∆ABC, B=90, AB=1, BC=√2-1, tanA=BC/AB=√2-1, AC=√(AB^2+BC^2)=√(1+2+1-2√2)=√(4-2√2).

cotA=1/tanA=1/(√2-1)=√2+1=2.4142 approx (multiply top and bottom by √2+1: (√2+1)(√2-1)=2-1=1).

cosecA=1/sinA=AC/BC=√(4-2√2)/(√2-1)=√((4-2√2)/(√2-1)^2)=√((4-2√2)/(3-2√2))=√((4-2√2)(3+2√2))=√(12+2√2-8)=√(4+2√2)=2.6131 approx.