Question

plz solve what is in the photo ​

Answer 1

Explanation :

Refer to the attachment

Some important identities :

★ CosecØ = 1/SinØ

★ CotØ = CosØ/SinØ

★ TanØ = 1/CotØ

★ Sin²Ø + Cos²Ø = 1

★ Sec²Ø - Tan²Ø = 1

★ Cosec²Ø - Cot²Ø = 1

★ SinØ = Cos(90 - Ø)

★ CosØ = Sin(90 - Ø)

★ TanØ = Cot(90 - Ø)

★ CotØ = Tan(90 - Ø)

★ CosecØ = Sec(90 - Ø)

★ SecØ = Cosec(90 - Ø)

Answer 2

★ Question:

to prove :

$\frac{cot(x) \times \cos(x) }{1 + \sin(x) } = \csc(x) - 1$

★ Answer :

LHS =

$\frac{ \cot(x) \times cos(x) }{1 + \sin(x) }$

$= \frac{ \frac{ \cos(x) }{ \sin(x) } \times \cos(x) }{1 + \sin(x) }$

$= \frac{ \frac{ \cos {}^{2} ( x ) }{ \sin(x) } }{1 + \sin(x) }$

$= \frac{ \cos {}^{2} (x) }{(1 + \sin(x)) \sin(x) }$

use the forumla : cos²x = 1-sin²x

$= \frac{1 - \sin {}^{2} (x) }{(1 + \sin(x)) \sin(x) }$

we know that

a² -b² = (a+b) (a-b)

then ;

$= \frac{(1 + \sin(x)) (1 - \sin(x)) }{(1 + \sin(x)) \sin(x) }$

$= \frac{1 - \sin(x) }{ \sin(x) }$

$= \csc(x) - 1$

= RHS

•Hence ; proved

hope it helps you ! ☺️