Forum

(sin A + cosec A)^2...
 
Notifications
Clear all

(sin A + cosec A)^2 + (cos A + sec A)^2 = 7 + tan^2A + cot^2A

1 Posts
2 Users
0 Likes
197 Views
0
Topic starter

Evaluate:

(sin A + cosec A)+ (cos A + sec A)2 = 7 + tan2A + cot2A

1 Answer
0

(sin A + cosec A)+ (cos A + sec A)2 = 7 + tan2A + cot2A

L.H.S. = (sin A + cosec A)+ (cos A + sec A)2

It is of the form (a+b)2, expand it

(a+b)2 = a2 + b2 + 2ab

= (sin2A + cosec2A + 2 sin A cosec A) + (cos2A + sec2A + 2 cos A sec A)

= (sin2A + cos2A) + 2 sin A(1/sin A) + 2 cos A(1/cos A) + 1 + tan2A + 1 + cot2A

= 1 + 2 + 2 + 2 + tan2A + cot2A

= 7+tan2A+cot2A = R.H.S.

Therefore, (sin A + cosec A)+ (cos A + sec A)2 = 7 + tan2A + cot2A

Hence proved.

Share:

How Can We Help?