Question

tan (45° + ∅) + tan(45°- ∅) = 2sec2∅​

Answer 1

Answer:

2 sec2 theta

Step-by-step explanation:

Given

tan(45+ theta)+ tan (45-theta)

tan45+tan theta/ 1-tan45.tan theta=tan(45+theta)

tantan45-tan theta/ 1+ tan45.tan theta=tan(45-theta)

(1+ tan theta)(1+tan theta)+((1- tan theta)(1-tan theta)/(1+ tan theta)(1- tan theta

1+tan^2 theta+ 2 tan theta+1+tan^2 theta- 2 tan theta/(1- tan^2theta)

1+ tan^2 theta+1+tan^ 2 theta/(1- tan^2 theta)

2+2tan^2 theta/(1-tan^2theta)

2(1+tan^2theta)/(1-tan^2 theta)

2.1/(1-tan^2theta)/(1+tan^2theta)

2.1/cos2 theta

2. sec2theta