Question : The value of $\frac{3\left(\operatorname{cosec}^2 26^{\circ}- an ^2 64^{\circ} ight)+\left(\cot ^2 42^{\circ}-\sec ^2 48^{\circ} ight)}{\cot \left(22^{\circ}- heta ight)-\operatorname{cosec}^2\left(62^{\circ}+ heta ight)- an \left( heta+68^{\circ} ight)+ an ^2\left(28^{\circ}- heta ight)}$ is:
Option 1: 3
Option 2: 4
Option 3: –1
Option 4: –2

Question

Question : The value of $\frac{3\left(\operatorname{cosec}^2 26^{\circ}- an ^2 64^{\circ} ight)+\left(\cot ^2 42^{\circ}-\sec ^2 48^{\circ} ight)}{\cot \left(22^{\circ}- heta ight)-\operatorname{cosec}^2\left(62^{\circ}+ heta ight)- an \left( heta+68^{\circ} ight)+ an ^2\left(28^{\circ}- heta ight)}$ is:

Option 1: 3

Option 2: 4

Option 3: –1

Option 4: –2

Team Careers360 · Accepted Answer

Correct Answer: –2

Solution : $\frac{3\left(\operatorname{cosec}^2 26^{\circ}- an ^2 64^{\circ} ight)+\left(\cot ^2 42^{\circ}-\sec ^2 48^{\circ} ight)}{\cot \left(22^{\circ}- heta ight)-\operatorname{cosec}^2\left(62^{\circ}+ heta ight)- an \left( heta+68^{\circ} ight)+ an ^2\left(28^{\circ}- heta ight)}$
$= \frac{3\left(\operatorname{sec}^2 64^{\circ}- an ^2 64^{\circ} ight)+\left(\cot ^2 42^{\circ}-\operatorname{cosec} ^2 42^{\circ} ight)}{ an \left(68^{\circ}+ heta ight)-\operatorname{cosec}^2\left(62^{\circ}+ heta ight)- an \left( heta+68^{\circ} ight)+\cot ^2\left(62^{\circ}+ heta ight)}$
$= \frac{3\left(1 ight)+\left(\cot ^2 42^{\circ}-1-\cot ^2 42^{\circ} ight)}{-(\operatorname{cosec}^2\left(62^{\circ}+ heta ight)-\cot ^2\left(62^{\circ}+ heta ight))}$
$= \frac{3-1}{-1}$
$= -2$
Hence, the correct answer is –2.

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Question : The value of 3(cosec226∘−tan2⁡64∘)+(cot2⁡42∘−sec2⁡48∘)cot⁡(22∘−θ)−cosec2(62∘+θ)−tan⁡(θ+68∘)+tan2⁡(28∘−θ) is:Option 1: 3Option 2: 4Option 3: –1Option 4: –2

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Question : The value of $\frac{3 ({cosec}^{2} 26^{\circ} - \tan^{2} 64^{\circ}) + (\cot^{2} 42^{\circ} - \sec^{2} 48^{\circ})}{\cot (22^{\circ} - θ) - {cosec}^{2} (62^{\circ} + θ) - \tan (θ + 68^{\circ}) + \tan^{2} (28^{\circ} - θ)}$ is:
Option 1: 3
Option 2: 4
Option 3: –1
Option 4: –2