Question

lf a, b ,c are in $AP$ and the greatest angle is $A$, and the least angle is $C$, then $4(1-\cos A)(1-\cos B)$ is equal to

• A. $\cos A-\cos C$
• B. $\sin A-\sin C$
• C. $\sin A+\sin C$
• D. None of these

Answer 1

The correct option is D None of these

Since, a, b, c are in AP so according to Sine Rule, angle A,B,C are proportional to a, b, c as sine is an increasing function in $[0^o,{90}^o]$

So, A,B,C are also in AP.

Let us assume them to be ${90}^o,{60}^o,{30}^o$ which are in AP

and $4(1-\cos {90}^o)(1-\cos {60}^o)=2$

Since no option gives result $=2$ on putting above values

Therefore, Answer is $D$