Prove that- -sin- -cos- tan-1

(cosecθ sinθ) (secθ cosθ) (tanθ+ cotθ) =(1sinθ sinθ)(1cosθ cosθ)(sinθcosθ+cosθsinθ) =(1 sin^2θsinθ)(1 cos^2θcosθ)(sin^2θ+cos^2θsinθcosθ) = ...

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Standard X

Mathematics

Trigonometric Ratios of a Right Triangle

Prove that: ...

Question

Prove that:
$(csc θ - sin θ) (sec θ - cos θ) (tan θ - cot θ) = 1$

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Solution

$(c o s e c θ - s i n θ) (s e c θ - c o s θ) (t a n θ + c o t θ) = (\frac{1}{sin θ} - sin θ) (\frac{1}{cos θ} - cos θ) (\frac{sin θ}{cos θ} + \frac{cos θ}{sin θ}) = (\frac{1 - {sin}^{2} θ}{sin θ}) (\frac{1 - {cos}^{2} θ}{cos θ}) (\frac{{sin}^{2} θ + {cos}^{2} θ}{sin θ cos θ}) = \frac{{cos}^{2} θ . {sin}^{2} θ .1}{{sin}^{2} θ {cos}^{2} θ} = 1$

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Similar questions

Q. Prove the following identities (1-17)

(cosec θ - \sin θ) (\sec θ - \cos θ) (\tan θ + \cot θ) = 1

Evaluate,

(csc θ - sin θ) (sec θ - cos θ) (tan θ + cot θ) =

(cosec θ - sin θ) (sec θ - cos θ) (tan θ + cot θ) = . . . . . . .

Q. Prove that :

(sin θ + cos θ) (tan θ + cot θ) = sec θ + csc θ

(a) Prove that $\frac{c o s A}{1 + s i n A} + t a n A = s e c A$

(b) Prove the identity $(s i n θ + c o s θ) (t a n θ + c o t θ) = s e c θ + c o s e c θ$ [6 MARKS]

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Prove that:(cscθ−sinθ) (secθ−cosθ) (tanθ−cotθ)=1

(cosecθ−sinθ)(secθ−cosθ)(tanθ+cotθ)=(1sinθ−sinθ)(1cosθ−cosθ)(sinθcosθ+cosθsinθ)=(1−sin2θsinθ)(1−cos2θcosθ)(sin2θ+cos2θsinθcosθ)=cos2θ.sin2θ.1sin2θcos2θ=1

Prove that:
$(csc θ - sin θ) (sec θ - cos θ) (tan θ - cot θ) = 1$