Question

If I = m secA + n tanA and k = n secA + m tanA, then
(1) l2+ k2 = m2 + n2
(2) l2 - k2 = m2 + n2
(3) l2 - k2 = m2 - n2
(4) l2 + k2 = m2 -n2​

Answer 1

Answer:

I = m secA + n tanA....................(i)

K= n secA + m tanA....................(ii)

Squaring (i) and (ii) both Sides,We get;

I² = m² sec ² A + n² tan ² A...................(iii)

K²= n² sec² A + m² tan² A..................(iv)

Subtracting (iv) from (iii)

I² - K² = (m² sec² A + n² tan² A) - (n² sec² A + m² tan²A)

I²- K² = m² sec²A + n² tan² A - n² sec²A - m² tan²A

I²- K²= m² sec²A - m² tan²A - n² sec² A + n² tan²A

I²- K²= m²(sec²A - tan²A) - n²( sec²A - tan² A)

I²- K²= m²- n²

Hence Ans (4) is the correct answer

I²- K²= m²- n²