Question

cosx+sinx/cosx-sinx=8, then cotx ?​

Answer 1

Answer:

Cos x + sin x / cos x - sin x = 8

Cos x + sin x / cos x - sin x = 8By componendo & dividendo,

Cos x + sin x / cos x - sin x = 8By componendo & dividendo,(Cos x + sin x )+(cos x - sin x)/(Cos x + sin x) -(cos x - sin x) = (8+1)/(8–1)

Cos x + sin x / cos x - sin x = 8By componendo & dividendo,(Cos x + sin x )+(cos x - sin x)/(Cos x + sin x) -(cos x - sin x) = (8+1)/(8–1)=> 2cosx/2sinx = 9/7

Cos x + sin x / cos x - sin x = 8By componendo & dividendo,(Cos x + sin x )+(cos x - sin x)/(Cos x + sin x) -(cos x - sin x) = (8+1)/(8–1)=> 2cosx/2sinx = 9/7=> cotx= 9/7

Answer 2

Answer:

ANSWER

∣sinx−cosx∣=

(sinx−cosx)

2

=

sin

2

x+cos

2

x−2sinxcosx

=

1−2sinxcosx

Given sinx+cosx=a

squaring both sides we get

(sinx+cosx)

2

=a

2

⇒sin

2

x+cos

2

x+2sinxcosx=a

2

⇒1+2sinxcosx=a

2

⇒2sinxcosx=a

2

−1

∴∣sinx−cosx∣=

1−(a

2

−1)

=

2−a

2