# Thread: trig compound angle formulae and proofs

1. ## trig compound angle formulae and proofs

Hi I've got some maths homework and stuck on the last 3 questions.

1. Given that sinA=3/5 and cosB=12/13, where A is obtuse and B is acute, find exact values of
a) cos(A+B)
b)cot (A-B)

2. Prove cot(A+B)is identical to cotAcotB-1
cotA+cotB
3. prove that tanA+tanB is identical to sin(A+B)
cosAcosB

I have tried all these and just get stuck .

any help would be really appreciative

thankyou

2. 1) $\cos A=-\sqrt{1-\sin^2A}, \ \sin B=\sqrt{1-\cos^2B}$

$\cos(A+B)=\cos A\cos B-\sin A\sin B$

$\cot(A-B)=\frac{\cos(A-B)}{\sin(A-B)}=\frac{\cos A\cos B+\sin A\sin B}{\sin A\cos B-\sin B\cos A}$

2) $\cos(A+B)=\frac{\cos(A+B)}{\sin(A+B)}=\frac{\cos A\cos B-\sin A\sin B}{\sin A\cos B+\sin B\cos A}=$

$=\frac{\frac{\cos A\cos B}{\sin A\sin B}-1}{\frac{\sin A\cos B}{\sin B\sin A}+\frac{\sin B\cos A}{\sin A\sin B}}=\frac{\cot A\cot B-1}{\cot A+cot B}$

3) $\tan A+\tan B=\frac{\sin A}{\cos A}+\frac{\sin B}{\cos B}=\frac{\sin A\cos B+\sin B\cos A}{\cos A\cos B}=\frac{\sin(A+B)}{\cos A\cos B}$

3. ## thankyou

thanks so much. not sure if i get questions 1 yet though, i'll try it.