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```TRIGONOMETRIC RATIOS & IDENTITIES
Ex.7
If tan
1
=
Let
tan
2
1
=x=
=
1
2
2 x
2
x2 + 2x â 1 = 0
sin 4
a
1
1
2
tan
(0, 2 ), find the possible values of .
1
2
Sol.
where
1
2
Page # 151
2
x=
=
=
2 1
cos 4
b
1
2
8
or
=(
2 1)
sin 8
cos 8
a3
b3
1
If
Sol.
Given
sin 4
a
or,
or,
or,
or,
or,
b(a + b) sin4
b(a + b) sin4
(a + b)2 sin4
(a + b)2 sin4
[(a + b) sin2
+ a(a + b) (1 â sin2 )2 = ab.
+ a(a + b) (1 + sin4 â 2sin2 ) = ab
â 2a (a + b) sin2 + a2 + ab = ab
â 2(a + b) sin2 . a + a2 = 0
â a]2 = 0
or,
(a + b) sin2
âa=0
Now,
sin8
a3
Ex.9
If â
2
<x<
cos 4
b
+
2
2 1 is not b/w (0, 2 )
9
8
Ex.8
a b
, prove that
8
b )3
(a
1
a b
cos8
b3
=
sin2 =
a4
b4
+
(a b )4 .a 3
(a b ) 4 b 3
a
cos2 =
a b
=
b
a b
a
b
a b
1
+
=
=
( a b )4
(a b )4
(a b )4
( a b )3
and y = log10(tan x + sec x). Then the expression E =
10 y
10
2
y
simplifies to one of the
six trigonometric functions. find the trigonometric function.
Sol.
y = log10 (tan x + sec x),
E=
=
10 y
10
2
y
y = log10
1 sin x
= cos x
cos x
1 sin x
2
1 sin x
cos x
=
1 sin2 x 2 sin x cos2 x
2 cos x(1 sin x)
2 sin x (1 sin x )
2 sin2 x 2 sin x
=
= tan x
2
cos x (1 sin x )
2 cos x(1 sin x )
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```
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