Question

Prove that (1 + cot
- cosec
) + (1 + tan 8 + sec 0 ) = 2.​

Answer 1

Correct Question:

Prove that ( 1 + cotA - cosecA ) + ( 1 + tanA + secA ) = 2

Solution:

L.H.S. = ( 1 + cotA - cosecA )( 1 + tanA + secA )

$= (1 + \frac{cosA}{sinA} - \frac{1}{sinA} )(1 + \frac{sinA}{cosA} + \frac{1}{cosA} )$

$= ( \frac{sinA + cosA - 1}{sinA} )( \frac{cosA + sinA + 1}{cosA} )$

$= \frac{(sinA + cosA) {}^{2} - 1 {}^{2} }{sinAcosA}$

$= \frac{sin {}^{2}A + cos {}^{2}A + 2sinAcosA - 1 }{sinAcosA }$

$= \frac{1 + 2sinAcosA - 1}{sinAcosA \: }$

$= \frac{2sinAcosA \: }{sinAcosA \: }$

= 2 = R.H.S

$\huge{\blue{\boxed{\boxed{\boxed{\pink{\underline{\underline{\mathfrak{\red{♡Hence\: Proved♡}}}}}}}}}}$