e) Show that $$ \sin heta(1+ an heta)+\cos heta(1+\cot heta)=\sec heta+\csc heta $$ f) (i) Express $$ \sin ^{2} heta $$ in terms of $$ \cos 2 heta $$. (ii) Use your answer to (i) to prove the identity:

Question

e) Show that $$ \sin 	heta(1+	an 	heta)+\cos 	heta(1+\cot 	heta)=\sec 	heta+\csc 	heta $$ f) (i) Express $$ \sin ^{2} 	heta $$ in terms of $$ \cos 2 	heta $$. (ii) Use your answer to (i) to prove the identity:

UpStudy AI · Accepted Answer

To prove the identity $$ \sin 	heta(1+	an 	heta)+\cos 	heta(1+\cot 	heta)=\sec 	heta+\csc 	heta $$, we start by rewriting the left-hand side using the definitions of tangent and cotangent. After simplifying and applying the Pythagorean identity, we show that the left-hand side equals the right-hand side, thus proving the identity. For part f (i), we express $$ \sin^2 	heta $$ in terms of $$ \cos 2	heta $$ using the double angle identity for cosine.

e) Show that \( \sin \theta(1+\tan \theta)+\cos \theta(1+\cot \theta)=\sec \theta+\csc \theta \) f) (i) Express \( \sin ^{2} \theta \) in terms of \( \cos 2 \theta \). (ii) Use your answer to (i) to prove the identity:

UpStudy ThothAI Solution

Quick Answer

Step-by-step Solution

e) Show that \( \sin \theta(1+\tan \theta)+\cos \theta(1+\cot \theta)=\sec \theta+\csc \theta \) f) (i) Express \( \sin ^{2} \theta \) in terms of \( \cos 2 \theta \). (ii) Use your answer to (i) to prove the identity:

UpStudy ThothAI Solution

Quick Answer

Step-by-step Solution

Related Questions