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`tan theta = 3tanB``3tan theta = tanC``(6tan theta)/(tan^(2)theta-9) = tanA``angle B = angleC`

Answer :

A::C::D**For all values of angle A and B `(i)cos(A-B)=cosAcosB+sinAsinB
(ii) cos(A+B)=cosAcosB-sinAsinB`**

**For all values of angle A and B `(i)sin(A-B)=sinAcosB-cosAsinB (ii)sin(A+B)=sinAcosB+cosAsinB`**

** Geometric representation of sine and cosine of angles**

**For all values of A and B `tan(A+B)=(tanA+tanB)/(1-tanAtanB)` and `tan(A-B)=(tanA-tanB)/(1+tanAtanB)`**

**Prove that `sin(A+B)sin(A-B)=sin^2A-sin^2B=cos^2B-cos^2A`**

**Prove that `cos(A+B)cos(A-B)=cos^2A-sin^2B=cos^2B-sin^2A`**

**Prove that `sin(A+B+C)=sinAcosBcosC+cosAsinBcosC+cosAcosBsinC-sinAsinBsinC` `cos(A+B+C)=cosAcosBcosC-cosAsinBsinC-sinAcosBsinC-sinAsinBcosC`**

**Prove that `tan(A+B+C)=(tanA+tanB+tanC-tanAtanBtanC)/(1-tanAtanB-tanBtanC-tanCtanA)`**

**`(i) cos75^@ (ii)cos15^@`**

**`(i) cos 15^@ (ii) cos75^@ (iii) tan15^@ (iv)tan75^@`**