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liraira [26]
3 years ago
9

SHOW STEPS PLEASE!!!

Mathematics
1 answer:
Sholpan [36]3 years ago
6 0
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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