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natima [27]
3 years ago
8

Prove that

Mathematics
1 answer:
Dovator [93]3 years ago
5 0

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identities

secx = \frac{1}{cosx} , cosecx = \frac{1}{sinx}

cotx = \frac{cosx}{sinx} , tanx = \frac{sinx}{cosx}

Consider the left side

secA cosecA - cotA

= \frac{1}{cosA} × \frac{1}{sinA} - \frac{cosA}{sinA}

= \frac{1}{cosAsinA} - \frac{cosA}{sinA}

= \frac{1-cos^2A}{cosAsinA}

= \frac{sin^2A}{cosAsinA} ( cancel sinA on numerator/ denominator )

= \frac{sinA}{cosA}

= tanA = right side ⇒ proven

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