Prove the identity: ( \sin \theta+\cos \theta)(\tan \theta+\cot \theta) = \sec \theta+{\cosec} \theta

ICSE Class X Math 2014 Solved Paper - Question 51

Question : 51 of 52

Marks: +1, -0

Prove the identity:

( sin \;θ+\cos θ)(\tan θ+\cot θ)

=\ sec θ+{\cosec} θ

Solution:

\;\text " L.H.S. "\;\;=( sin \;θ+\cos θ)(\tan θ+\cot θ)

\;=( sin \;θ+\cos θ) (\;{ sin \;θ}/{\cos θ}+\;{\cos θ}/{ sin \;θ})

\;=( sin \;θ+\cos θ) (\;{ sin \;^2 θ+\cos ^2 θ}/{\cos θ sin \;θ})

\;=( sin \;θ+\cos θ) × \;{1}/{\cos θ sin \;θ}

\;=\;{ sin \;θ}/{\cos θ sin \;θ}+\;{\cos θ}/{\cos θ sin \;θ}

\;=\;{1}/{\cos θ}+\;{1}/{ sin \;θ}=\ sec θ+{\cosec} θ

\;=\;\text " R.H.S. "\;

Go to Question:

Prev Question

Next Question