Question

please help prove it​

Answer 1

Step-by-step explanation:

[cos x + sin x + 1 + cos x + sin x -1]/(cos x + sin x)²-1

[ by taking LCM and (a + b)(a - b) = a² - b² ]

=> 2(cos x + sin x)/cos²x + sin²x + 2sin x cos x - 1

=> 2(cos x + sin x)/1 + 2 sin x cos x - 1

=> 2(cos x + sin x)/2 sin x cos x

=> (cos x + sin x)/sin x cos x

=> cos x / sin x cos x + sin x /sin x cos x

=> 1/sin x + 1/cos x

=> cosec x + sec x