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Please help me with this !! Cos 2 76 + Cos 2 16 – Cos76.Cos16

Please help me with this !!
 
Cos276 + Cos216 – Cos76.Cos16
 

Question Image
Grade:11

2 Answers

Lab Bhattacharjee
121 Points
4 years ago
\text{Use } \cos^2x+\cos^2(60^\circ+x)=1+\cos^2x-\sin^2(60^\circ+x) \\ =1+\cos(x+60^\circ +x)\cos(60^\circ+x-x)=? \\ 2\cos(x+60^\circ +x)\cos x=\cos(x+60^\circ +x)+\cos(60^\circ+x-x)=? \\ \text{Here }x=16^\circ
Ajay
209 Points
4 years ago
Here is correct way to find
Since Cos A =  (1+ Cos 2A)/2 we can write as follows
 =  (1+ Cos 152)/2 +  (1 + cos 32)/2  – Cos 76 Cos 16
=  1 + ½ (cos 152 + Cos 32)  – Cos 76 Cos 16
= 1 + ½ ( 2 Cos 92. Cos 60) – 1/2(Cos 60 + Cos 92) 
Put cos 60 = 1/2
= 1 +  ½ * cos92 – 1/2(1/2 + Cos 92)
1 + ½ cos 92 – ¼ –  ½ Cos 92
= 3/4

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