Question

if x=asec teta+b tan teta,y=a tan teta +bsec teta then prove that x^-y^=a^-b^​

Answer 1

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Question

If x = a secθ + b tanθ , y = a tanθ + b secθ

then prove that x² - y² = a² - b² .

Solution

Given

x = a secθ + b tanθ

y = a tanθ + b secθ

To prove

x² - y² = a² - b²

Proof

Taking LHS

LHS = x² - y²

= (a secθ + b tanθ)² - ( a tanθ + b secθ)²

=a²sec²θ+b²tan²θ+2 ab secθtanθ - (a²tan²θ+b²sec²θ+2 ab tanθsecθ

= a²sec²θ +b²tan²θ +2 ab secθ tanθ - a²tan²θ -b²sec²θ -2 ab tanθsecθ

= a²sec²θ + b²tan²θ -a²tan²θ - b²sec²θ

= a²( sec²θ -tan²θ) + b²(tan²θ - sec²θ )

(by trigonometric identity

sec²α - tan²α = 1  ,and

tan²α - sec²α = -1 ., so we will get)

= a² ( 1 ) + b² ( - 1 )

= a² - b²

= RHS

LHS = RHS

Proved.

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Answer 2

Answer:

My self Amit

Class 10

Step-by-step explanation:

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