How can you prove sinθ+cotθ(both over)/cosθ = tanθ+cscθ?
1 Answer
Mar 26, 2018
Verified, step by step below...
Explanation:
-
Split the numerator
#sintheta/costheta+cottheta/costheta= tantheta+csctheta# -
Apply the quotient identity:
#tantheta= sintheta/costheta#
#tantheta+cottheta/costheta= tantheta+csctheta# -
Apply the quotient identity:
#cottheta= costheta/sintheta# |
#tantheta+(costheta/sintheta)/costheta= tantheta+csctheta# -
Simplify
#tantheta+(cancelcostheta/sintheta)*1/cancelcostheta= tantheta+csctheta#
- Apply the reciprocal identity:
#1/sintheta= csctheta#
#tantheta+csctheta= tantheta+csctheta#