Question

1 + sin x
18. If<x<a and
= k secx, then k =
2.
1-sin x
1 + sin x 1-sin x
19. If <x< 1 and
+
2
V1-sin x 1+ sin x
= k se
1 + COS X
+
V1-COS X
20. If < x < 21 and
=k
1-COS X
1 + COS X X​

Answer 1

Answer:

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Answer 2

Answer:

Answer

Given that,

1+sinx

1−sinx

=secx−tanx

Squaring both sides, we get

1−sinx

1+sinx

=(secx+tanx)

2

R.H.S=(secx+tanx)

2

=(secx+tanx)(secx+tanx)

=sec

2

x+2secxtanx+tan

2

x

=

cos

2

x

1

+2.

cosx

1

.

cosx

sinx

+

cos

2

x

sin

2

x

=

cos

2

x

1+2sinx+sin

2

x

=

1−sin

2

x

(1+sinx)(1+sinx)

=

(1+sinx)(1−sinx)

(1+sinx)(1+sinx)

=

1−sinx

1+sinx

∴(secx−tanx)

2

=

1+sinx

1−sinx

⇒secx−tanx=

1+sinx

1−sinx

=L.H.S

Step-by-step explanation:

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