27. If x= p tan 0 + q sec 0 and y= p sec 0 + q tan 0 then prove that x² - y2 = q2 -p2
Answers
Answered by
0
Answer:
We have ,
L.H.S=
x
2
a
2
−
y
2
b
2
⇒L.H.S=
a
2
sin
2
θ
a
2
−
b
2
tan
2
θ
b
2
[∵x=asinθ,y=btanθ]
⇒L.H.S=
sin
2
θ
1
−
tan
2
θ
1
⇒L.H.S=cosec
2
θ−cot
2
θ [∵1+cot
2
θ=cosec
2
θ∴cosec
2
θ−cot
2
θ=1]
⇒ LHS =1= RHS
Hence, proved
Step-by-step explanation:
please mark brainliest
Answered by
2
Answer:
True
Step-by-step explanation:
x² = p² tan² + q² sec² + 2 pq tan . sec
y² = p² sec² + q² tan² + 2 pq tan . sec
x² + y² = p² (tan² -sec² ) + q² (sec² -tan² )
= p² (-1) + q² [ - (tan² - sec² ) ]
= - p² + q² [ - (-1) ]
= - p² + q²
= q² - p² Proved.
Similar questions