Question

sin theeta =cos theeta , then the value of tan^2 theeta + cot^2 theeta =?​

Answer 1

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Given

sin θ + cos θ = √2

To find,

tanθ + cot θ =?

Soluchan:-

sin θ + cos θ = √2

Squaring on both sides,

= ( sin θ + cos θ )² = √2²

= (sin² θ + cos² θ )+ 2 sin θ cos θ = 2

= 1+ 2sin θ cos θ = 2

⇒ sin θ cos θ = 1/2

Now,

tanθ + cot θ =sin θ/cos θ + cos θ/sin θ

=( sin² θ +cos² θ) / sin θ cos θ

= 1 / (1/2) = 2 (answer)

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