Question

please give the solution of these three questions I will shourly mark your answer as brainlist


Question 1. if 5x=secQ and 5/x = tanQ then find the value of 5[x^2-1/x^2]

Question 2. Express secQ in terms of cotQ

Question 3. Find the value of cosQ cos(90-Q)-sinQ sin(90-Q)

Answer 1

$\textbf{- Answers -}$

$\textbf{(1)}$

Given,

5x = secQ and 5/x = tanQ

⇒ x = secQ/5 and 1/x = tanQ/5

Now,

5 (x² - 1/x²)

= 5 [{(secQ)/5}² - {(tanQ)/5}²]

= 5 {(sec²Q)/25 - (tan²Q)/25}

= 5/25 (sec²Q - tan²Q)

= 1/5

$\textbf{(2)}$

Now, secQ

= √(1 + tan²Q), since sec²θ - tan²θ = 1

= √{1 + 1/(cot²Q)}

$\textbf{(3)}$

Now,

cosQ cos(90 - Q) - sinQ sin(90 - Q)

= cosQ sinQ - sinQ cosQ

= 0

#$\textbf{MarkAsBrainliest}$