1 answer:
Tanθ + cotθ = 1/sinθcos<span>θ
since we know that;
tan</span>θ = sinθ/cos<span>θ, and
cot</span>θ = cosθ/sin<span>θ
now when we add tan</span>θ and cot<span>θ and replace their values;
tan</span>θ + cot<span>θ=sin</span>θ/cosθ + cosθ/sin<span>θ
</span>For a common denominator to add those two fractions, the obvious choice is sinθ.cosθ , so
tanθ + cotθ = sin²θ/sinθcosθ + cos²θ/sinθcosθ =sin²θ + cos²θ / sinθcosθ
now we can use the identity that;
sin²θ + cos²θ = 1
So,
tanθ + cotθ = 1/sinθcosθ
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