Question

What is the value of tan’A - sec’A, if Oºs A< 90° ?
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Answer 1

Answer:

- 1

Step-by-step explanation:

Correct Question :-

What is the value of $tan^2A-sec^2A$ , If $0\degree<A<90\degree$ ?

To Find :-

Value of $tan^2A-sec^2A$ Where $0\degree<A<90\degree$

Solution :-

We know that :-

$sin^2A+cos^2A=1$

Dividing the whole equation with "cos^2A" :-

$\dfrac{sin^2A+cos^2A}{cos^2A}=\dfrac{1}{cos^2A}$

$\dfrac{sin^2A}{cos^2A}+\dfrac{cos^2A}{cos^2A},= \dfrac{1}{cos^2A}$

$\bigg(\dfrac{sinA}{cosA}\bigg)^2+1=\bigg(\dfrac{1}{cosA}\bigg)^2$

We know that :-

1) sinA/cosA = tanA

2) 1/cosA = secA

$(tanA)^2+1=(secA)^2$

$tan^2A + 1 = sec^2A$

$tan^2A-sec^2A = -1$

Since, $tan^2A - sec^2A = -1$

Trigonometric Identities :-

$1)sin^2A+cos^2A = 1$

$2)sec^2A-tan^2A=1$

$3)csc^2A-cot^2A=1$