271)

If \(sec^2θ+tan^2 = 7\), then the value of θ where 0° ≤ θ ≤ 90° is 

A)

60°

B)

30°

C)

0°

D)

90°

272)

If \(7sin^2θ+3cos^2 θ = 4\) (0° ≤ θ ≤ 90°), then value of θ is 

A)

π/4

B)

 π/2

C)

 π/6

D)

 π/3

273)

If \(\alpha+\theta= {7 \pi \over 12}\) and tanθ = √3, then the value of tanα is 

A)

1/√3

B)

0

C)

√3

D)

1

274)

sin (A+B) = 1 and cos (A-B) = √3/2, where A & B are positive acute angles with A ≥ , then A and B are: 

A)

A = 75°, B = 15°

B)

A = 60°, B = 30°

C)

A = 45°, B = 45°

D)

None of these.

275)

If \(2sin^2 \theta-3sin\theta + 1 = 0;\) θ being positive acute angle(s), then the value of θ is/are 

A)

30°, 90°

B)

60°, 75°

C)

60°, 45°

D)

45°, 90°

276)

If sin\({(60°-\theta)}\)=cos\({(\psi-30°)}\), then the value of tan \({(\psi-\theta)}\) is {assume that \(\theta\) and \(\psi\) are both positive acute angels with \(\theta<60°\) and \(\psi>30°)\).

A)

\(1\over \sqrt{3}\)

B)

0

C)

\( \sqrt{3} \)

D)

1

 

277)

Evaluate: 3 cos 80° cosec 10° + 2 cos 59° cosec 31°

A)

1

B)

3

C)

2

D)

5

278)

If \({ sec^270° -cot^220°\over2{(cosec^259°-tan^231°)} }= {2 \over m}\)then m is equal to:

A)

2

B)

3

C)

4

D)

1

279)

If \(\alpha+\beta=90°\) , then the value of ​​​​​\({(1-sin^2\alpha)(1-cos^2\alpha)*(1+cot^2\beta)(1+tan^2 \beta)}\) is.

A)

1

B)

-1

C)

0

D)

2

280)

If \(sin21°={x\over y}\), then \(sec21°-sin69°\) is equal to

A)

\(x^2\over{y}\sqrt{y^2-x^2}\)

B)

\(x^2\over{y}\sqrt{x^2-y^2}\)

C)

\(y^2\over{x}\sqrt{x^2-y^2}\)

D)

\(y^2\over{x}\sqrt{y^2-x^2}\)