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
Answers
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Answer:
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Answered by
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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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