Question

if sintheta + cos theta = root2 the prove that tan theta + cot theta =2

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Answer 1

Answer:

here given ...

sin θ + cos θ = √2

we have to find

tanθ + cot θ =?

solution:-

sin θ + cos θ = √2

now square on both side

= ( 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

Step-by-step explanation:

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Answer 2

Answer:

sin@ + cos@ = √2

=> sin²@ + 2sin@cos@ + cos²@ = 2

=> 1+2sin@cos@ = 2

=> 2sin@cos@ = 1

=> sin@cos@ = 1/2 ........... @1

=> tan@ + cot@

= sin@/cos@ + cos@/sin@

=(sin²@ + cos²@)/sin@cos@

= 1/sin@cos@

=>1/(1/2) (from equation 1)

=2