How we caluclate tan40,52degree

Use Maclaurin series for the expansion of tangent function.

where x is the angle in radians

x = 40 degrees = (40/180) pi = (2/9)pi = 0.7 radians (approx)

tan(40 ^o ) = 0.7 + (0.7) ³   /3 + 2 (0.7) ⁵   /15 + 17 (0.7) ⁷   /315 + .......... neglecting the higher degrees.

tan(40 ^o ) = 0.7 + 0.11433 + 0.0224 + 0.004

tan(40 ⁰   ) = 0.84 (approx)

Similarly, you can find the value of tan 52⁰