Question

show that cot theta + Tan theta = Sec theta Cosec theta​

Answer 1

Answer:

Step-by-step explanation:

In R. H. S

cot A+tan A

we can write this as cos A ÷ sin A +sin A ÷ cosA

so,

cosA²+sinA²÷sinA*×cosA

cos A²+sinA²=1

1÷sinA×cosA

now,

1÷sinA×1÷cosA

cosecA × secA

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Answer 2

Solution:-

cotθ + tanθ = secθ × cosecθ

L.H.S.

=) cotθ + tanθ

=) cosθ/sinθ + sinθ/cosθ

=) [ ( cos²θ + sin²θ )/ (sinθ. cosθ ) ]

=) 1/ sinθ. cosθ

=) 1/sinθ. 1/cosθ

=) cosecθ. secθ

L.H.S. = R.H.S.

Hence Proved!

Identity Used:-

• ( sin²θ + cos²θ ) = 1
• cotθ = cosθ/sinθ
• tanθ = sinθ/cosθ
• 1/sinθ = cosecθ
• 1/cosθ = secθ