Question

proof lhs=rhs..............

Answer 1

Kindly refer to attachment plzzz!!!


Hope it helps *_*

Answer 2

Prove L.H.S =R.H.S:

Step-by-step explanation:

$\ Given \ equation:\\\\(cot A\ + sec B)^2 -(tan B\ - cosec A)^2 = 2(cot A. sec B + tan B . Cosec A)\\\\\ Solution:\\\\\ solve \ L.H.S \ part:\\\\\rightarrow (cot \ A\ + sec \ B)^2 -(tan \ B\ - cosec \ A)^2 \\\\\rightarrow (cot \ A)^2\ + (sec \ B)^ + 2.cot \ A. sec \ B \ - ( (tan \ B)^2\ + (cosec \ A)^2 - 2. tan \ B. cosec \ A )\\\\\rightarrow (cot \ A)^2\ + (sec \ B)^2 + 2.cot \ A. sec \ B \ - (tan \ B)^2\ - (cosec \ A)^2 + 2. tan \ B. cosec \ A )$

$\rightarrow (cot \ A)^2\ - (cosec \ A)^2 + (sec \ B)^2 - (tan \ B)^2 \ + 2.cot \ A. sec \ B \ + 2. tan \ B. cosec \ A ) \\\\\therefore cosec \ A^2 - cot \ A^2 =1 \ \ \ and \ \ sec \ B^2 - tan \ B^2 \ = 1\\\\\because \ common (-) \rightarrow (cot \ A)^2\ - (cosec \ A)^2 \\\\ \rightarrow -(cosec \ A^2 - cot \ A^2)\ \ which \ is = \ -1\\\\ \rightarrow -1 +1 \ + 2.cot \ A. sec \ B \ + 2. tan \ B. cosec \ A ) \\\\\rightarrow 2.cot \ A. sec \ B \ + 2. tan \ B. cosec \ A )$

$\rightarrow 2(cot \ A. sec \ B \ + tan \ B. cosec \ A )$

L.H.S= R.H.S

Learn more:

• L.H.S= R.H.S: https://brainly.in/question/14989805
• Simplify: https://brainly.in/question/15529362