Question

(1-cos A)(1+ sec A)= tan A × din A​

Answer 1

Answer:

hope it will help you:-)

Answer 2

❥${\underline{\underline{\large{\mathtt{QUESTION:-}}}}}$

Prove that,

$\sf{(1-cosA)(1+secA)\:=tanA\times\:sinA}$

❥${\underline{\underline{\large{\mathtt{SOLUTION:-}}}}}$

Taking L.H.S,

$\sf{(1-cosA)(1+secA)}$

★We know secA =$\sf\frac{1}{cosA}$★

$\implies\sf{(1-cosA)(1+\frac{1}{cosA})}$

$\implies\sf{(1-cosA)(\frac{cosA+1}{cosA})}$

$\implies\sf\frac{(1-cosA)(1+cosA)}{cosA}$

$\implies\sf\frac{1-cos^2A}{cosA}$

★We know 1-cos²A = sin²A★

$\implies\sf\frac{sin^2A}{cosA}$

$\implies\sf{sinA\times\:\frac{sinA}{cosA}}$

$\implies\sf{sinA\times\:tanA\:(Proved)}$

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

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MORE INFORMATION:-

Some formulas related to trigonometry:-

• sin²A + cos²A = 1
• 1 + tan²A = sec²A
• 1+cot²A = cosec²A

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