Question

If sin A+cos A=3/2 then find the value of sum of all trigonometric ratios with angle A
plz anwer this...I need it urgently...

Answer 1

Answer:

Step-by-step explanation:

Step-by-step explanation:

Hi,

Given sin A + cos A = 3/2

Now squaring on both sides we get

sin²A + cos²A +2 sin A cos A = 9/4

⇒ 1 + 2 sin A cos A = 9/4

⇒2 sin A cos A = 5/4

⇒ sin A cos A = 5/8

Now,

Consider sin A + cos A + tan A + cot A + cosec A + sec A

= (sin A + cos A) + (sin A/cos A + cos A/sin A) + (1/sin A + 1/ cos A)

=(sin A + cos A) + (sin²A + cos²A)/sin A cos A + (sin A + cos A)/sin A cos A

= 3/2 + 8/5 + 8/5*3/2

= 3/2 + 8/5 + 12/5

= 11/2

Hope, it help