Prove that, `(tanA+tanB)/(tanA-tanB)=(sin(A+B))/(sin(A-B))`

Prove that, tan3A.tan2A.tanA=tan3A-tan2A-tanA

Prove that (tanA+secA-1)/(tanA-secA+1)=(1+sinA)/(cosA) Thinking Process : Here, use the formula i.e., sec^(2)A-tan^(2)A=1anda^(2)-b^(2)=(a+b)(a-b) to solve the above problems.

Prove that, sinA+sinB+sinC-sin(A+B+C)= 4sin((A+B)/(2))sin((B+C)/(2))sin((C+A)/(2))

Using vector, Prove that for DeltaABC , (a)/(sinA)=(b)/(sinB)=( c )/(sin C) .

(tanA+secA-1)/(tanA-secA+1)=(cosA)/(1-sinA)

By using above basic addition/ subtraction formulae, prove that (i) tan (A+B)=(tan A+tan B)/(1-tan A tan B) , (ii) tan (A-B)=(tan A-tanB)/(1+tan A tan B) (iii) sin2theta=2sintheta costheta , (iv) cos2theta=cos^(2)theta=1-2sin^(2)theta=2cos^(2)theta-1 (v) tan 2theta=(2 tan theta)/(1-tan^(2) theta)

Prove that, (cosA-cosB)^(2)+(sinA-sinB)^(2)=4sin^(2)((A-B)/(2))

If sin2A= lambda sin 2B prove that (tan(A+B)/tan(A-B))=(lambda+1)/(lambda-1)

For DeltaABC , prove that, (a+b)/(c)=(cos((A-B)/(2)))/(sin""(C)/(2)) .

Prove that, a^(3)sin(B-C)+b^(3)sin(C-A)+c^(3)sin(A-B)=0