Hi brainlies!!Pls help me with this question:-
Q. If cosec θ- sin θ= a³ and sec θ- cos θ= b³, then prove that a²b²(a²+b²)= 1..
.
.try only if u know the correct answer.
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Answers
Answered by
5
Answer:
Given : cosecθ−sinθ=a
3
and secθ−cosθ=b
3
⇒
sinθ
1
−sinθ=a
3
⇒
sinθ
cos
2
θ
=a
3
⇒a=(
sinθ
cos
2
θ
)
3
1
Similarly ; b=(
cosθ
sin
2
θ
)
3
1
⇒a
2
b
2
(a
2
+b
2
)=a
4
b
2
+a
2
b
4
⇒(
sinθ
cos
2
θ
)
3
4
(
cosθ
sin
2
θ
)
3
2
+(
sinθ
cos
2
θ
)
3
2
(
cosθ
sin
2
θ
)
3
4
⇒(cosθ)
8/3−2/3
.(sinθ)
4/3−4/3
+(sinθ)
8/3−2/3
.(cosθ)
4/3−4/3
⇒cos
2
θ+sin
2
θ=1
⇒a
2
b
2
(a
2
+b
2
)=1
Answered by
6
Step-by-step explanation:
done prapti . and thnk my ans ❤️ and good night prapti
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