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महाराष्ट्र राज्य शिक्षण मंडळएस.एस.सी (इंग्रजी माध्यम) इयत्ता १० वी

If Cosθ = 5 13 , Then Find Sinθ.

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प्रश्न

If cosθ = `5/13`, then find sinθ. 

बेरीज
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उत्तर

cosθ = `5/13`

`sin^2θ + cos^2θ = 1`

`sin^2θ + (5/13)^2 = 1`

`sin^2θ = (1 - 25)/169`

`sin^2θ = (169 - 25)/169`

`sin^2θ = 144/169`

sinθ = `sqrt(144/169)`

sinθ = `12/13`

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2018-2019 (July) Set 1

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संबंधित प्रश्‍न

Prove the following trigonometric identities

If x = a sec θ + b tan θ and y = a tan θ + b sec θ, prove that x2 − y2 = a2 − b2


if `x/a cos theta + y/b sin theta = 1` and `x/a sin theta - y/b cos theta = 1` prove that `x^2/a^2 + y^2/b^2  = 2`


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`sqrt((1 - cos^2theta) sec^2 theta) = tan theta` 


Find the value of sin2θ  + cos2θ

Solution:

In Δ ABC, ∠ABC = 90°, ∠C = θ°

AB2 + BC2 = `square`   .....(Pythagoras theorem)

Divide both sides by AC2

`"AB"^2/"AC"^2 + "BC"^2/"AC"^2 = "AC"^2/"AC"^2`

∴ `("AB"^2/"AC"^2) + ("BC"^2/"AC"^2) = 1`

But `"AB"/"AC" = square and "BC"/"AC" = square`

∴ `sin^2 theta  + cos^2 theta = square` 


Statement 1: sin2θ + cos2θ = 1

Statement 2: cosec2θ + cot2θ = 1

Which of the following is valid?


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