Question : The value of $\frac{3\left(\cot ^2 47^{\circ}-\sec ^2 43^{\circ}\right)-2\left(\tan ^2 23^{\circ}-\operatorname{cosec}^2 67^{\circ}\right)}{\operatorname{cosec}^2\left(68^{\circ}+\theta\right)-\tan \left(\theta+61^{\circ}\right)-\tan ^2\left(22^{\circ}-\theta\right)+\cot \left(29^{\circ}-\theta\right)}$ is:
Option 1: –1
Option 2: 1
Option 3: 5
Option 4: 0
Latest: SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL complete guide
Correct Answer: –1
Solution :
Given: $\frac{3\left(\cot ^2 47^{\circ}-\sec ^2 43^{\circ}\right)-2\left(\tan ^2 23^{\circ}-\operatorname{cosec}^2 67^{\circ}\right)}{\operatorname{cosec}^2\left(68^{\circ}+\theta\right)-\tan \left(\theta+61^{\circ}\right)-\tan ^2\left(22^{\circ}-\theta\right)+\cot \left(29^{\circ}-\theta\right)}$
= $\frac{3\left(\cot ^2(90^{\circ}- 43^{\circ})-\sec ^2 43^{\circ}\right)-2\left(\tan ^2 23^{\circ}-\operatorname {cosec^2} (90^{\circ}-23^{\circ})\right)}{\sec^2\left(90^{\circ}-(68^{\circ}+\theta)\right)-\cot \left(90^{\circ}-(\theta+61^{\circ})\right)-\tan ^2\left(22^{\circ}-\theta\right)+\cot \left(29^{\circ}-\theta\right)}$
= $\frac{3\left(\tan ^243^{\circ}-\sec ^2 43^{\circ}\right)-2\left(\tan ^2 23^{\circ}-\sec^2 23^{\circ}\right)}{\sec^2\left(22^{\circ}-\theta\right)-\cot \left(29^{\circ}-\theta\right)-\tan ^2\left(22^{\circ}-\theta\right)+\cot \left(29^{\circ}-\theta\right)}$
= $\frac{(3× -1)-(2×(-1))}{1}$
= $\frac{-3+2}{1}$
= $-1$
Hence, the correct answer is –1.
Related Questions
Question : The value of
Know More about
Staff Selection Commission Combined Grad ...
Answer Key | Eligibility | Application | Selection Process | Preparation Tips | Result | Admit Card
Get Updates Brochure
Your Staff Selection Commission Combined Graduate Level Exam brochure has been successfully mailed to your registered email id “”.
