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Byju's Answer
Standard XII
Mathematics
Trigonometric Ratios of Compound Angles
Simplify the ...
Question
Simplify the following expression
sin
2
θ
+
cos
2
θ
sin
θ
+
cos
θ
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Solution
On simplifying, we get
sin
2
θ
+
cos
2
θ
sin
θ
+
cos
θ
...........As,
(
s
i
n
2
x
+
c
o
s
2
x
=
1
)
⟹
1
sin
θ
+
cos
θ
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Similar questions
Q.
Simplify:-
sin
θ
+
cos
θ
sin
θ
−
cos
θ
+
sin
θ
−
cos
θ
sin
θ
+
cos
θ
=
2
sin
2
θ
−
cos
2
θ
Q.
Solve the following equations:
(i)
cos
θ
+
cos
2
θ
+
cos
3
θ
=
0
(ii)
cos
θ
+
cos
3
θ
-
cos
2
θ
=
0
(iii)
sin
θ
+
sin
5
θ
=
sin
3
θ
(iv)
cos
θ
cos
2
θ
cos
3
θ
=
1
4
(v)
cos
θ
+
sin
θ
=
cos
2
θ
+
sin
2
θ
(vi)
sin
θ
+
sin
2
θ
+
sin
3
=
0
(vii)
sin
θ
+
sin
2
θ
+
sin
3
θ
+
sin
4
θ
=
0
(viii)
sin
3
θ
-
sin
θ
=
4
cos
2
θ
-
2
(ix)
sin
2
θ
-
sin
4
θ
+
sin
6
θ
=
0
Q.
Prove that
sin
θ
−
cos
θ
sin
θ
+
cos
θ
+
sin
θ
+
cos
θ
sin
θ
−
cos
θ
=
2
sin
2
θ
−
cos
2
θ
Q.
Solve:
sin
θ
sin
2
θ
=
cos
θ
cos
2
θ
Q.
Show that none of the following is an identity:
(i) cos
2
θ + cos θ = 1
(ii) sin2θ + sin θ = 2
(iii) tan
2
θ + sin θ = cos
2
θ
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