Question

यदि 5secθ - 12cosecθ = 0 हो तो secθ, cosθ तथा sinθ का मान ज्ञात कीजिए। 

Answer 1

5secθ - 12cosecθ = 0

∴ 5secθ = 12cosecθ

∴ `(secθ)/(cosecθ) = 12/5`

∴ secθ ÷ cosecθ = `12/5`

∴ `1/costheta ÷ 1/sinθ = 15/5` .........`[sectheta = 1/costheta, cosectheta = 1/sintheta]`

∴ `1/costheta xx sintheta/1 = 12/5`

∴ `sintheta/costheta = 12/5`

∴ tanθ = `12/5`

1 + tan²θ = sec²θ 

∴ `1 + (12/5)^2 = sec^2theta`

∴ `sec^2theta = 1 + 144/25`

∴ `sec^2theta = (25 + 144)/25`

∴ `sec^2theta = 169/25`

∴ secθ = `13/5` .............(दोनों पक्षों का वर्गमूल लेने पर)

∴ cosθ = `1/sectheta`

∴ cosθ = `1/((13/5))`

∴ cosθ = `5/13`

`sin^2theta + cos^2theta = 1`

∴ `sin^2theta + (5/13)^2 = 1`

∴ `sin^2theta + 25/169 = 1`

∴ `sin^2theta = 1 - 25/169`

∴ `sin^2theta = (169 - 25)/169`

∴ `sin^2theta = 144/169`

∴ `sintheta = 12/13` ...............(दोनों पक्षों का वर्गमूल लेने पर)

`sectheta = underline(13/5), costheta = 5/13` और `sintheta = underline(12/13).`