Question

prove that
$\frac{cot a + coseca - 1}{cota - coseca + 1} = \frac{1 + cosa}{sina}$

Answer 1

Answer: Proof Below

Step-by-step explanation:

cosec A + cot A - 1 / cot A - cosec A + 1 

WE KNOW THAT,cosec ² A - cot ² A = 1 

SUBSTITUTING THE ABOVE EQUATION IN NUMERATOR

cosec A + cot A -(cosec ² A - cot ² A) / (cot A - cosec A + 1) 

x²-y²= (x+y)(x-y) 

cosec A + cot A - (cosec A + cot A) (cosec A - cot A) / (cot A - cosec A + 1) 

=>(cosec A + cot A)(1-cosec A + cot A) / (cot A - cosec A + 1) 

= cosec A + cot A 

= 1/sin A + cos A/sin A 

= (1+cos A) / sin A