Answer to Question #87429 in Trigonometry for Mr Y

Question

13. If A =600 , B=450 and C=300, Prove that
tan2A + 4cos2B +3 sec3C=9 where, 600 is 60 degree,450 is 45 deg 300 is 30 deg and tan 2 is tan square cos2 and sec 3 is all square and cube

Answer 1

Solution

If A = 60°, B= 45° , C=30° then

tan A = tan 60°=sqrt(3)

cos B = cos 45°= sqrt(2)/2

sec C = sec 30°=2/sqrt(3)

Substitute:  tan²A+4cos²B+3sec³C=(sqrt(3))²+4*(sqrt(2)/2)²+3*(2/sqrt(3))³=3+4*2/4+3*8/3sqrt(3)=3+2+8/sqrt(3)=9