Question

if A=60degree and B= 30degree then prove that tan(A-B) =tanA-tanB /1+tanAtanB​

Answer 1

A = 60

B=30

tan(A-B)= tanA-tanB/1+tanA tanB--eq(1)

substitute A and B in equity(1)

tan(60-30)=tan60- tan30 /1+ tan60tan30-----eq(2)

we know that

tan60=✓3. tan30=1/✓3

substitute these values in equity(2)

tan30= ✓3-1/✓3÷1+✓3×1/✓3

3-1/✓3÷1+1 = 2//✓3÷2

=1/✓3(tan30)

hence proved