Question

(1/sec k-tan k)-(1/cos k)=(1/cos k)-(1/sec k+ tan k)

Answer 1

Answer:

Given, LHS = 1 / seck - tank - 1/cosk

By Rationalizing LHS we will get,

1/ seck - tank * seck + tank/ seck + tank 1

- 1/cosk

= seck + tank / sec²k - tan²k - 1/ cosk

[ ( a + b ) ( a - b ) = a² - b² ]

= 1 /cosk - 1/cosk + tank = tank

Similarly, RHS = 1/cosk - 1/seck + tank

Rationalizing RHS, we will get,

1/cosk - 1/seck + tank * seck - tank/ seck - tank

= 1/cosk - seck - tank / sec²k - tan²k

[ ( a + b ) ( a - b ) = a² - b² ]

= 1/cosk - ( seck - tank)

= 1/ cosk - 1/cosk + tank

= tank

Hence, LHS = RHS

(HENCE PROVED)

PLEASE MARK AS BRAINLIEST

Answer 2

$\large\bf{\underline\orange{❥solution:-}}$

❥Given, LHS = 1 / seck - tank - 1/cosk

❥By Rationalizing LHS we will get,

❥1/ seck - tank * seck + tank/ seck + tank 1

- 1/cosk

= seck + tank / sec²k - tan²k - 1/ cosk

[ ( a + b ) ( a - b ) = a² - b² ]

= 1 /cosk - 1/cosk + tank = tank

❥Similarly, RHS = 1/cosk - 1/seck + tank

❥Rationalizing RHS, we will get,

❥1/cosk - 1/seck + tank * seck - tank/ seck - tank

= 1/cosk - seck - tank / sec²k - tan²k

❥[ ( a + b ) ( a - b ) = a² - b² ]

= 1/cosk - ( seck - tank)

= 1/ cosk - 1/cosk + tank

= tank

❥Hence, LHS = RHS