If a tan = b, then value of a cos2 + b sin2 is
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Answered by
1
is equal to;; 388338382
Answered by
0
Answer:
Correct option is
B
a
Given:- tanθ=
a
b
To find:- acos2θ+bsin2θ=?
Sol:-
As we know that,
sin2θ=
1+tan
2
θ
2tanθ
cos2θ=
1+tan
2
θ
1−tan
2
θ
Therefore,
acos2θ+bsin2θ
=a(
1+tan
2
θ
1−tan
2
θ
)+b(
1+tan
2
θ
2tanθ
)
=a
⎝
⎜
⎜
⎜
⎜
⎜
⎜
⎛
1+(
a
b
)
2
1−(
a
b
)
2
⎠
⎟
⎟
⎟
⎟
⎟
⎟
⎞
+b
⎝
⎜
⎜
⎜
⎜
⎜
⎜
⎛
1+(
a
b
)
2
2(
a
b
)
⎠
⎟
⎟
⎟
⎟
⎟
⎟
⎞
=a(
a
2
+b
2
a
2
−b
2
)+b(
a
2
+b
2
2ab
)
=
a
2
+b
2
a
3
−ab
2
+2ab
2
=
a
2
+b
2
a
3
+ab
2
=
a
2
+b
2
a(a
2
+b
2
)
=a
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