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Prove that sinA - cosA + 1 / sinA + cos A - 1 = 1/secA -tanA ​​

Answer»

Answer:

sin a ( 1+ SINA / cos a )  + cos a ( 1+ cos a / sin a )

sin a ( (cos a + sin a ) / cos a )  + cos a ((sin a + cos a) / sin a )

(cos a + sina )(sin a / cos  a )  +  (sin a + cos a )(cos a / sin a )

(cos a + sin a)(tan a ) + (cos a + sin a)(cot a )

taking cos a + sin a as COMMON we get

(cos a + sin a )(tan a + cot a )

(cos a + sin a )((sin a / cos a)+(cos a / sin a ))

(cos a + sina )((sin2a + cos 2A / sin a cos a))

(cos a + sin a )( 1 / sin a cos a)

(cos a + sina ) /  sin a cos a

(cos a / sin a cos a)  + (sin a / sin a cos a )

( 1 / sin a ) + (1 / cos a )

cosec a + sec a

hence proved

Step-by-step EXPLANATION:

I THINK so !!


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