Question

Prove that tan 75 degrees=2+√3.
Can anybody help me to solve this?

Answer 1

Answer:

LHS = tan75

= tan(45+30)

= (tan45+tan30)/(1-tan45tan30)

= (1+1/√3)(1-1/√3)

= ((√3+1)/√3)/ ((√3-1)/√3)

= (√3+1)/(√3-1)

= (√3+1)/(√3-1)×(√3+1)/(√3+1) (rationalising)

= (√3+1)²/(√3²-1²)

= (3+2√3+1)/(3-1)

= (4+2√3)/2

= 2(2+√3)/2

= 2+√3 = RHS

Typed a lot, it would have been better if I would have solved in the notebook and uploaded it rather than to solve and type in this.