If Psin60
∘
=Qcsc45
∘
, then the value of
P
2
−Q
2
P
2
+Q
2
is equal to:
- A11
5
- B7
11
- C5
11
- D11
7
Solution & Step-by-step Explanation
We know the standard trigonometric values:
sin60
∘
=
2
3
csc45
∘
=
2
Given:
P×
2
3
=Q×
2
Q
P
=
3
2
2
Squaring both sides:
Q
2
P
2
=
(
3
)
2
(2
2
)
2
=
3
8
Using componendo and dividendo or simple substitution (P
2
=8k, Q
2
=3k):
P
2
−Q
2
P
2
+Q
2
=
8−3
8+3
=
5
11
sin60
∘
=
2
3
csc45
∘
=
2
Given:
P×
2
3
=Q×
2
Q
P
=
3
2
2
Squaring both sides:
Q
2
P
2
=
(
3
)
2
(2
2
)
2
=
3
8
Using componendo and dividendo or simple substitution (P
2
=8k, Q
2
=3k):
P
2
−Q
2
P
2
+Q
2
=
8−3
8+3
=
5
11