If cos(A-B)=35andtanAtanB=2, then which one of the following is correct?
sin(A+B)=15
sin(A+B)=-15
cos(A–B)=-15
cos(A+B)=-15
The explanation for the correct option:
Finding the value:
Given,
cos(A–B)=35….(i)tanAtanB=2sinAcosA×sinBcosB=21
Using componendo and dividendo rule,
⇒(sinAsinB+cosAcosB)(sinAsinB–cosAcosB)=(2+1)(2–1)cos(A–B)-cos(A+B)=3-35cos(A+B)=3[∵From(i)]cos(A+B)=-15
Hence, the correct option is option (D).
If cosA=−2425 and cosB=35, where π<A<3π2 and 3π2<B<2π, find the following: (i)sin(A+B) (ii)cos(A+B)
If x1=√a+3b+√a−3b√a+3b−√a−3b then, which one of the following statements is true?
If 5a+2b5a−2b=53, then a : b =