Question

If sinA + cosA = a, tanA + cotA = b, show that (a^2 –1)/2 =1/b

Answer 1

Step-by-step explanation:

sinA + cosA = a    ............(1)

tanA + cotA = b    ............(2)

(a² - 1)/2 = 1/b      

solve L.H.S

(a² - 1)/2

put the value of from equation (1)

{(sinA +cosA)² - 1)}/2

(sin²A +cos²A +2sinAcosA -1)/2

(1 + 2sinAcosA - 10/2

(2sinAcosA)/2

sinAcosA (L.H.S)

Solve R.H.S

tanA + cotA

sinA/cosA + cosA/sinA

(sin²A + cos²A)/sinAcosA

1/sinAcosA = 1/b

(a² - 1)/2 = 1/b  

sinAcosA = 1/sinAcosA