How to prove 5secx+4 =9secsquarex- 4tansquarex?
#5sec^2x+4 =9sec^2x- 4tan^2x?#
3 Answers
Please find a Proof in Explanation.
Explanation:
I hope, the Question is to prove :
If we use the Identity :
can be easily proved as follows :
Otherwise,
The question is in error, and in fact
# 5sec^2x+4 -= 9sec^2x-4tan^2x #
Explanation:
The question is in error, and in fact
# 5sec^2x+4 -= 9sec^2x-4tan^2x #
As can be shown, if we consider the LHS:
# LHS -= 5sec^2x+4 #
# \ \ \ \ \ \ \ \ = 5(1+tan^2x)+4 #
# \ \ \ \ \ \ \ \ = 5+5tan^2x+4 #
# \ \ \ \ \ \ \ \ = 9+5tan^2x #
# \ \ \ \ \ \ \ \ = 9+5tan^2x + 4tan^2x - 4tan^2x#
# \ \ \ \ \ \ \ \ = 9+9tan^2x - 4tan^2x#
# \ \ \ \ \ \ \ \ = 9(1+tan^2x) - 4tan^2x#
# \ \ \ \ \ \ \ \ = 9sec^2x - 4tan^2x#
# \ \ \ \ \ \ \ \ -= RHS \ \ \ \ \ # QED
Answer for the question :
Please see below
Explanation:
We know that,
We have to prove,
We take,