Trigonometry Class XI

If  $\sin\theta+\operatorname{cosec}\theta=2$ , then $\sin^2\theta+\operatorname{cosec}^2\theta$    is equal to 

• 1

• 4

• 2

• none of these

If  $f\left(x\right)=\cos^2x+\sec^2x\ ,\$  then 

•  $f\left(x\right)<1$  

•  $f\left(x\right)=1$  

•  $2<f\left(x\right)<1$  

•  $f\left(x\right)\ge2$  

If $\tan\theta=\frac{1}{2}\ and\ \ \tan\phi=\frac{1}{3},$  then the value of 

 $\theta+\phi$  is 

•  $\frac{\pi}{6}$  

•  $\pi$  

•  $0$  

•  $\frac{\pi}{4}$  

Which of the following is not correct ?

• 
  

  $\sin\theta=-\frac{1}{5}$
  

• $\cos\theta=1$

• $\sec\theta=\frac{1}{2}$

• $\tan\theta=20$

The value of $\tan1\degree\ .\ \tan2\degree\ .\ \tan3\degree\ .\ ......\ .\ \tan89\degree$ is  

• 0

• 1

•  $\frac{1}{2}$  

• none of these

 $The\ value\ of\frac{1-\tan^215\degree}{1+\tan^215\degree}\ is$  

•  $1$  

•  $\sqrt{3}$  

•  $\frac{\sqrt{3}}{2}$  

•  $2$  

 $The\ value\ of\ \cos1\degree.\cos2\degree.\cos3\degree.\ \ ...\ \ .\ \cos179\degree\ is$  

•  $\frac{1}{\sqrt{2}}$  

•  $0$  

•  $1$  

•  $-1$  

 $If\ \tan\theta=3\ and\ \theta\ lies\ in\ third\ quadrant,\$  

 $then\ the\ value\ of\ \sin\theta\ is$  

•  $\frac{1}{\sqrt{10}}$  

•  $-\frac{1}{\sqrt{10}}$  

•  $-\frac{3}{\sqrt{10}}$  

•  $\frac{3}{\sqrt{10}}$  

The value of

 $\sin^2\ 75\degree-\sin^2\ 15\degree$  is 

•  $\frac{1}{2}$  

•  $\frac{\sqrt{3}}{2}$  

•  $1$  

•  $0$  

 $\ \frac{\cos10\degree+\sin10\degree}{\cos10\degree-\sin10\degree}$  is equal to 

•  $\tan55\degree$  

•  $\cot55\degree$  

•  $-\tan55\degree$  

•  $-\cot55\degree$