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Answer 1

Answer:

b/√a²+b²

Step-by-step explanation:

         Given,  tanθ = a/b

We would like to solve it using identities which include tan and cos,  such as:     1 + tan²θ = sec²θ    

⇒  1 + tan²θ = 1/cos²θ

⇒ cos²θ = 1/(1 + tan²θ)

          Therefore,   in this question

⇒ cos²θ = 1/( 1 + (a/b)² )

⇒ cos²θ = b²/(a² + b²)

⇒ cosθ = b/√(a² + b²)

              Hence the correct option is D.

Answer 2

tanθ = a/b ____[given]

as , 1 + tan²θ = sec²θ

and, secθ = 1/cosθ

cos²θ = 1/(1 + tan²θ)

= 1/[1 + (a/b)²]

= 1/(b²+a²/b²)

= b²/a²+b²

by taking Square root ,

cosθ = b/√(a² + b²) ✓ correct answer