Question

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PLZ SOLVE

If a²sec²∅ - b²tan²∅ = c² , prove that

sin²∅ = c² - a²/c² - b²



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Answer 1

Heya

_______________________________

We know that Sec² x = 1/Cos² x

And

Tan² x = Sin² x / Cos² x

______________________________

L.H.S

Let Angle be = x

=>

a² - b² Sin² x
__________ = c²
Cos² x

=>

a² - b² Sin²x = c² { 1 - Sin² x }

becoz { Cos² x = 1 - Sin² x }

=>

a² - c² = b² Sin² x - c² Sin² x

=>

a² - c² = Sin ² x { b² - c² }

=>

Sin² x = { a² - c² }/ { b² - c² }

=>

Sin² x = -{ c² - a² }/ -{ c² - b² }

=>

Sin² x = { c² - a² }/ { c² - b² }

Hence, proved.