Question

4
4
COS α
+
If
sina
= 1, then prove that
cos?B sin’B
cos B sinº B
= 1
cosa sin
sina
+​

Answer 1

Answer:LHS=cos  

2

A+cos  

2

B+2cosAcosB+sin  

2

A+sin  

2

B−2sinAsinB

(cos  

2

A+sin  

2

A)+(cos  

2

B+sin  

2

B)+2cosAcosB−2sinAsinB

2+2cosAcosB−2sinAsinB

2+cos(A+B)+cos(A−B)−cos(A−B)+cos(A+B)

2+2cos(A+B)          (∴cosx=2cos  

2

 

2

x

​  

−1)

2+2[2cos  

2

 

2

(A+B)

​  

−1]

2+4cos  

2

 

2

(A+B)

​  

−2=4cos  

2

 

2

(A+B)

​  

=R.H.S

Hence proved.

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