Find the value of sec (1275)

Ans:## – (2sqrt2)/(1 + sqrt3)##

##sec (1275) = 1/(cos 1275)##. First find ##cos (1275).##

##cos 1275 = cos (195 + 1080) = cos (195 + 3(360)) = cos (195).##

##cos 195 = cos (60 + 135) = cos 60.cos 135 – sin 60.sin 135 =##

##= (1/2)(-sqrt2/2) – (sqrt3/2)(sqrt2/2) = – (sqrt2/4)(1 + sqrt3)##

##sec 1275 = 1/(cos 195) = – 4/((sqrt2)(1 + sqrt3)) = -(2sqrt2)/(1 + sqrt3##

Check by calculator.

cos 195 = -0.97

cos 195 = – (1 + sqrt3)/(2sqrt2) = -(2.73)/(2.82) = – 0.97. OK