# Find #tan theta# if #sec theta = 17^2# ?

##### 1 Answer

Jun 21, 2018

# tantheta = +-24sqrt(145) ~~ 288.998#

#### Explanation:

We are given that

Using the trigonometric identity:

# 1 + tan^2A -= sec^2A #

we have:

# 1 + tan^2theta = (17^2)^2 #

# :. tan^2theta = 83521 - 1 #

# :. tan^2theta = 83520 #

# :. tantheta = +-sqrt(83520) #

# :. tantheta = +-24sqrt(145) #