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swat32
2 years ago
7

(1+tan^2 A)cot A/cosec^2 A= tanA​

Mathematics
1 answer:
Rufina [12.5K]2 years ago
4 0

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identities

1 + tan²A = sec²A , secA = \frac{1}{cosA}, cosecA = \frac{1}{sinA} , cotA = \frac{cosA}{sinA} , tanA = \frac{sinA}{cosA}

Consider the left side

\frac{(1+tan^2A)cotA}{cosec^2A}

= \frac{sec^2AcotA}{cosec^2A}

= \frac{\frac{1}{cos^2A}(\frac{cosA}{sinA})  }{cosec^2A}

= \frac{\frac{1}{cosAsinA} }{\frac{1}{sin^2A} }

= \frac{1}{cosAsinA} × sin²A

= \frac{sinA}{cosA}

= tanA = right side , thus proven

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