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SSC CHSL 2021 PYQ — Question 55

SSC CHSL - 5 Aug 2021 - Shift 2 • Quantitative Aptitude • Q55

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The value of  3tan260°+sec230°−sin245°(cos15°+sin75°)(sec15°+cosec75°){{3tan^260°+sec^230°-sin^245°} \over (cos15°+sin75°)(sec15°+cosec75°)}is

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Correct answer: D

Explanation

The correct answer is Option 4 i.e. 5924{{59} \over 24}

Concept USed:

cos(90 - A) = sinA

sec(90 - A) = cosecA

Explanation:

According to the given question,

3tan260°+sec230°−sin245°(cos15°+sin75°)(sec15°+cosec75°){{3tan^260°+sec^230°-sin^245°} \over (cos15°+sin75°)(sec15°+cosec75°)}

Putting the values of tan60°, sec30° and sin45°, we get

⇒3(3)2+(23)2−(12)2(cos(90°−75°)+sin75°)(sec(90°−75°)+cosec75°){{3({\sqrt{3})}^2+({2 \over \sqrt{3}})^2-({1 \over \sqrt{2}})^2} \over (cos(90° - 75°)+sin75°)(sec(90° - 75°)+cosec75°)}

Now, 9+43−12(sin75°+sin75°)(cosec75°+cosec75°){9+{4 \over3} - {1 \over 2} \over (sin 75° +sin75°)(cosec 75°+cosec75°)}

⇒ 596(2×sin75°)(2×cosec75°){{59 \over 6} \over (2 \times sin 75°)(2 \times cosec 75°)}

⇒ 5964{{59 \over 6} \over 4}

⇒ 5924{59 \over 24}

Hence the required answer is 5924{59 \over 24} .