Question

its of 15 points
pls it's urgent....solve it​

Answer 1

Required Answer:-

Given Information:

• sec(θ) - tan(θ) = 4

To prove:

• cos(θ) = 8/17

Proof:

Given that,

➡ sec(θ) - tan(θ) = 4 ......(i)

We know that,

➡ sec²(θ) - tan²(θ) = 1

➡ (sec(θ) + tan(θ))(sec(θ) - tan(θ)) = 1

Putting the values of sec(θ) - tan(θ), we get,

➡ 4(sec(θ) + tan(θ)) = 1

➡ sec(θ) + tan(θ) = 1/4 ......(ii)

Adding equations (i) and (ii), we get,

➡ 2sec(θ) = 4 + 1/4

➡ 2sec(θ) = 17/4

➡ sec(θ) = 17/8

➡ 1/cos(θ) = 17/8

➡ cos(θ) = 8/17 (Hence Proved)

Formula Used:

• sec²(θ) - tan²(θ) = 1

Relationship Between Trigonometric Functions:

• sin(θ) = 1/cosec(θ)
• cos(θ) = 1/sec(θ)
• tan(θ) = 1/cot(θ)
• sin(θ)/cos(θ) = tan(θ)

Answer 2

Answer:

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