# How to prove 5secx+4 =9secsquarex- 4tansquarex?

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#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 :** **Problem**

can be **easily proved** as follows :

**as desired!**

**Otherwise,**

**rest** is **as above.**

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,