State whether the following statements are true or false. Justify your answer.
(i) sin (A + B) = sin A + sin B.
(ii) The value of sin θ increases as θ increases.
(iii) The value of cos θ increases as θ increases.
(iv) sin θ = cos θ for all values of θ.
(v) cot A is not defined for A = 0°.
Answers
Answered by
1
Answer:
(i) False
sin(A+B)=sinA+sinB
A=45
o
,B=45
o
LHS: sin(45
o
+45
o
)=sin90
o
=1
RHS : sinA+sinB=
2
1
+
2
1
=
2
2
=
2
LHS
=RHS
(ii) True
sin0
o
=0sin30
o
=
2
1
=sin45
o
=
2
1
,sin60
o
=
2
3
sin90
o
=1
∴θ increase ans value of sinθ also increase.
(iii) False
cos0=1,cos30=
2
13
,cos45=
2
1
cos60=
2
1
,cos90=0
Value of cosθ does not increase from 0<0<90
o
(iv) False
This is true for θ=45
o
Let θ=90
o
sin90=1,cos90=0
(v) True
cotA=
sinA
cosA
cot0
o
=
sin0
cos0
=
0
1
=not defined
Answered by
4
Answer:
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