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If Sin =a^2-b^2\a^2+b^2 , find the …

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If Sin =a^2-b^2\a^2+b^2 , find the value of other five trigonometric ratios

Posted by Rajat Arora 4 years, 11 months ago

CBSE > Class 10 > Mathematics

2 answers

Rajat Arora 4 years, 11 months ago

In ΔABC, Let ∠ABC be θ Sin θ = (a2 - b2) / (a2 + b2) ⇒ AB = (a2 - b2) ⇒ AC = (a2 + b2) ⇒ BC = √[(a2 + b2)2 - (a2 - b2)2] [According to Pythagoras theorem] ⇒ BC = √(4a2b2) ⇒ BC = 2ab Cos θ = 2ab / (a2 + b2) Tan θ = (a2 - b2) / 2ab. Cosec θ, Sec θ and Cot θ are the reciprocals of Sin θ, Cos θ, Tan θ respectively.

0Thank You

Gaurav Seth 4 years, 11 months ago

In ΔABC, Let ∠ABC be θ

Sin θ = (a² - b²) / (a² + b²)

⇒ AB = (a² - b²)

⇒ AC = (a² + b²)

⇒ BC = √[(a² + b²)² - (a² - b²)²] [According to Pythagoras theorem]

⇒ BC = √(4a²b²)

⇒ BC = 2ab

Cos θ = 2ab / (a² + b²)

Tan θ = (a² - b²) / 2ab.

Cosec θ, Sec θ and Cot θ are the reciprocals of Sin θ, Cos θ, Tan θ respectively.

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