Question

1/sec x (tan x + cot x ) =
Options in picture!
PLEASE EXPLAIN !

Answer 1

B

Explanation:

using the trigonometric identities

• cos x =
`(1)/(secx)`, sin x =
`(1)/(cscx)`

• tan x =
`(sinx)/(cosx)`, cot x =
`(cosx)/(sinx)`

the expression can be rewritten as

cos x(
`(sinx)/(cosx)` +
`(cosx)/(sinx)`)

distributing gives

sin x +
`(cos^2x)/(sinx)` ( expressing as a single fraction )

=
`(sin^2x+cos^2x)/(sinx)` =
`(1)/(sinx)` = csc x