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amit

· started a discussion

· 1 Months ago

In 4th option it is given root 3 theta (Question: 108537.0 )

But in solution 4th option is written as root 3 sin theta

Question:

Consider the following:

(i) If cot θ = x , then x + \(\cfrac{1}{x}\) = sec θ. cosec θ 

(ii) If \(x+ \cfrac{1}{x}\) = sinθ, then \(x^2+\cfrac{1}{x^2}\) = sin2  θ- 2

(iii) If x = p secθ and y= q tan θ, then x2q2–y2p2 = p2q2

(iv) The maximum value of cos\(\theta\) \(-\sqrt{3} \ Sin\)\(\theta\) is 3. 

Which of these are correct?

Options:
A) (i) and (ii)
B) (ii) and (iii)
C) (iii) and (iv)
D) (i), (ii) and (iii)
Solution:
Ans: (d)

(i) If cot \(\theta\) = x, then

 

= cosec \(\theta\) sec \(\theta\)

(i) is correct

(ii) \(sin\theta =x+\cfrac{1}{x}=cosec\theta\ sec\theta\)

Squaring both sides: 

\(x^2+\cfrac{1}{x^2}=\theta-2\)

\(\therefore\) (ii) is correct

(iii) x = p sec\(\theta\) and y = q tan\(\theta\) 

\(\therefore\) x2q2 – y2p2 = p2q2 sec2q – p2q2 tan2q = p2q2 (sec2q – tan2q) = p2q2

\(\therefore\) (iii) is correct

= 2 [cos 60° cos\(\theta\) – sin 60° sin\(\theta\)] = 2 cos (60° + \(\theta\))

\(\therefore\) Maximum value = 2 × 1 = 2

Hence, (i), (ii) and (iii) are correct but (iv) is incorrect

Knowledge Expert

· commented

· 1 Months ago

Dear Student
the error will be fixed soon
regards
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