Evaluate : sin A cos (A - B) - cos A sin (A - B).
O sin A
O sin B
O
COS A
O
COS B
Answers
Answer:
Given : sin(A+B)=sinAcosB+cosAsinB and
cos(A−B)=cosAcosB+sinAsinB
(i) To find : sin75
∘
Put A=30
∘
and B=45
∘
, then
sin(30
o
+45
o
)=sin75
∘
=sin30
∘
cos45
∘
+cos30
∘
sin45
∘
=(1/2)×(1/
2
)+(
3
/2)×(1/
2
)
=(1/2
2
)+(
3
/2
2
)
sin(75
o
)=
2
2
(1+
3
)
(ii) Find cos75
∘
Put A=45
∘
and B=30
∘
, then
cos(45
o
−30
o
)=cos15
∘
=cos45
∘
cos30
∘
+sin45
∘
sin30
∘
=(1/
2
)×(
3
/2)+(1/
2
)×(1/2)
=(
3
/2
2
)+(1/2
2
)
cos(15
o
)=
2
2
(1+
3
)
.
Step-by-step explanation:
Answer:
Given : sin(A+B)=sinAcosB+cosAsinB and
cos(A−B)=cosAcosB+sinAsinB
(i) To find : sin75 ∘
Put A=30
∘ and B=45 ∘ , then
sin(30 o +45 o )=sin75 ∘
=sin30 ∘ cos45 ∘ +cos30 ∘ sin45 ∘
=(1/2)×(1/ 2 )+( 3 /2)×(1/ 2 )
=(1/2 2 )+( 3 /2 2 ) sin(75 o )= 2
(1+ 3 )
(ii) Find cos75 ∘
Put A=45 ∘ and B=30 ∘ , then cos(45 o −30 o )
=cos15 ∘
=cos45 ∘ cos30 ∘+sin45 ∘sin30 ∘
=(1/ 2 )×( 3 /2)+(1/ )×(1/2)
=( 3 /2 2 )+(1/2 2 )cos(15 o )= 2 2(1+ 3)
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