Question

sin∅+ cos∅ = √2 sin (90-∅) then determine cot ∅

Answer 1

Answer:

tan+1=root2

tan=root2-1

cot=1/root2-1

Answer 2

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GIVEN:-

sinθ+cosθ = √2 sin( 90- θ)

REQUIRED TO FIND cotθ:

SOLUTION:-

sinθ+cosθ=√2sin(90-θ)

{•°• squaring both sides}

=>(sinθ+cosθ)²=(√2sin(90-θ))²

=>sin²θ+cos²θ+2sinθcosθ=2cos²θ

{•°• sin(90-θ)=cosθ}

=>1+2sinθcosθ=2cos²θ {•°•sin²θ+cos²θ=1}

=>2sinθcosθ=2cos²θ-1

=>2sinθcosθ=cos2θ {•°• cos2θ=2cos²θ-1}

=>sin2θ=cos2θ {•°• sin2θ=2sinθcosθ}

=>sin2θ/cos2θ=1

=>tan2θ=1 {•°•tanθ=sinθ/cosθ}

=>tan2θ= tan45°

=>2θ=45°

=>θ=45°/2 or π/8

so, cotθ= cot π/8 =√2+1

•°• cos22.5= √2+1

TO SEE HOW I FIND VALUE FOR cot22.5 refer above attachment!!

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