Question

1. if A, B, C are the interior angles of a triangle, prove that tan(B+C/2)=cotA/2
2. If cos A+secA =2 show that cos^nA+sec^nA=2

Answer 1

see the attached photo for answer

Answer 2

Answer:

1) A, B, C is the angle of a triangle

Sum of interior angle of triangle is 180°

A + B + C = 180

B + C = 180 - A

Divide equation by 2

(B + C)/2 = (180 - A)/2

tan (B + C)/2 = tan (90 - A/2)

tan (B + C)/2 = cot A/2

Hence proved

2) cos A+sec A =2

Let cos A = x, then Sec A = 1/x

x + 1/x = 2

Let x = 1

x^n + 1/x^n = (1)^n + 1/ (1)^n = 1 + 1 = 2

cos ^n A + Sec^n A = 2