Question

sin A( 1+tan A) + cos A( 1+cot A) = cosec A + sec A​

Answer 1

Answer:

Step-by-step explanation:

On solving L.H.S. ,

=> SinA( 1+ TanA ) + CosA ( 1 + cotA )

=> SinA + SinA*TanA + CosA + CosA*CotA

=> $SinA + (Sin^{2}A) / CosA + CosA + (Cos^{2}A) / SinA$

=>${SinA + (Cos^{2}A) / SinA } +{ (Sin^{2}A) / CosA + CosA }$

=> $(Sin^{2}A + Cos^{2}A) / SinA + ( Sin^{2}A + Cos^{2}A) / CosA$

=> 1/SinA + 1/CosA

=> CosecA + SecA

=> R.H.S

HENCE, PROVED

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