Question

if sec theta + cos Theta = root 5 then find the value of sec^2 theta + cos^2 theta

Answer 1

Step-by-step explanation:

as sec A = 1 / cos A

thus 1 + cos² A = √5

now squaring the above equation

1 + cos⁴ A + 2 cos² A = 5

now

1 + cos⁴ A / cos ² A

5 - 2cos² A / √5 - 1 is the required answer

Answer 2

The value of sec²θ + cos²θ = 3

Given :

sec θ + cos θ = √5

To find :

The value of sec² θ + cos² θ

Solution :

Step 1 of 2 :

Write down the given data

Here it is given that sec θ + cos θ = √5

Step 2 of 2 :

Find the value of the expression

sec² θ + cos² θ

= ( sec θ + cos θ )² - 2 × sec θ × cos θ

= (√5)² - 2 × 1

= 5 - 2

= 3

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ If cosθ+secθ=√2,find the value of cos²θ+sec²θ

https://brainly.in/question/25478419

2. Value of 3 + cot 80 cot 20/cot80+cot20 is equal to

https://brainly.in/question/17024513

3. In a triangle, prove that (b+c-a)(cotB/2+cotC/2)=2a×cotA/2

https://brainly.in/question/19793971