Question : The value of $\frac{3\left(\cot ^2 47^{\circ}-\sec ^2 43^{\circ} ight)-2\left( an ^2 23^{\circ}-\operatorname{cosec}^2 67^{\circ} ight)}{\operatorname{cosec}^2\left(68^{\circ}+ heta ight)- an \left( heta+61^{\circ} ight)- an ^2\left(22^{\circ}- heta ight)+\cot \left(29^{\circ}- heta ight)}$ is:
Option 1: –1
Option 2: 1
Option 3: 5
Option 4: 0

Question

Question : The value of $\frac{3\left(\cot ^2 47^{\circ}-\sec ^2 43^{\circ} ight)-2\left( an ^2 23^{\circ}-\operatorname{cosec}^2 67^{\circ} ight)}{\operatorname{cosec}^2\left(68^{\circ}+ heta ight)- an \left( heta+61^{\circ} ight)- an ^2\left(22^{\circ}- heta ight)+\cot \left(29^{\circ}- heta ight)}$ is:

Option 1: –1

Option 2: 1

Option 3: 5

Option 4: 0

Team Careers360 · Accepted Answer

Correct Answer: –1

Solution : Given: $\frac{3\left(\cot ^2 47^{\circ}-\sec ^2 43^{\circ} ight)-2\left( an ^2 23^{\circ}-\operatorname{cosec}^2 67^{\circ} ight)}{\operatorname{cosec}^2\left(68^{\circ}+ heta ight)- an \left( heta+61^{\circ} ight)- an ^2\left(22^{\circ}- heta ight)+\cot \left(29^{\circ}- heta ight)}$
= $\frac{3\left(\cot ^2(90^{\circ}- 43^{\circ})-\sec ^2 43^{\circ} ight)-2\left( an ^2 23^{\circ}-\operatorname {cosec^2} (90^{\circ}-23^{\circ}) ight)}{\sec^2\left(90^{\circ}-(68^{\circ}+ heta) ight)-\cot \left(90^{\circ}-( heta+61^{\circ}) ight)- an ^2\left(22^{\circ}- heta ight)+\cot \left(29^{\circ}- heta ight)}$
= $\frac{3\left( an ^243^{\circ}-\sec ^2 43^{\circ} ight)-2\left( an ^2 23^{\circ}-\sec^2 23^{\circ} ight)}{\sec^2\left(22^{\circ}- heta ight)-\cot \left(29^{\circ}- heta ight)- an ^2\left(22^{\circ}- heta ight)+\cot \left(29^{\circ}- heta ight)}$
= $\frac{(3× -1)-(2×(-1))}{1}$
= $\frac{-3+2}{1}$
= $-1$
Hence, the correct answer is –1.

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Question : The value of 3(cot2⁡47∘−sec2⁡43∘)−2(tan2⁡23∘−cosec267∘)cosec2(68∘+θ)−tan⁡(θ+61∘)−tan2⁡(22∘−θ)+cot⁡(29∘−θ) is:Option 1: –1Option 2: 1Option 3: 5Option 4: 0

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Question : The value of $\frac{3 (\cot^{2} 47^{\circ} - \sec^{2} 43^{\circ}) - 2 (\tan^{2} 23^{\circ} - {cosec}^{2} 67^{\circ})}{{cosec}^{2} (68^{\circ} + θ) - \tan (θ + 61^{\circ}) - \tan^{2} (22^{\circ} - θ) + \cot (29^{\circ} - θ)}$ is:
Option 1: –1
Option 2: 1
Option 3: 5
Option 4: 0