Question

Sin(90-A)+cos(180-2A)/cos(90-2A)+sin(180-A)

Answer 1

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Answer 2

Step-by-step explanation:

Given Sin(90-A)+cos(180-2A)/cos(90-2A)+sin(180-A)

• Now express in terms of A we get
• Cos A – cos 2A / sin 2A + sin A
• Now cos A – 2 cos^2 A + 1 = - (2 cos^2 A – cos A – 1)  -----------1
• Also denominator will be 2 sin A cos A + sin A = sin A (2 cos A + 1)
• Let cos A = x then 2 x^2 – x – 1
•                     = 2x^2 – 2x + x – 1
•                    = 2x (x – 1) + 1 (x – 1)
•                     = (2x + 1) (x – 1)
• So equation 1 can be written as  
•      = - (2 cos A + 1) ( cos A – 1) / sin A (2 cos A + 1)
•       = - cos A – 1 / sin A
•      = 1 – cos A / sin A
•    = 2 sin^2 A / 2 / 2 sin A / 2 cos A/2
•     = tan A/2

Reference link will be

https://brainly.in/question/4734658