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SSC CGL 2023 PYQ — Question 69

SSC CGL - 21 July 2023 - Shift 4 • Quantitative Aptitude • Q69

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Simplify 1+sint4−4sint−1−sint4+4sint\frac{1+sint}{4-4sint} -\frac{1-sint}{4+4sint}

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Correct answer: B

Explanation

The correct answer is option 2 i.e. tan t. sec t.

Given that

1+sint4−4sint−1−sint4+4sint\frac{1+sint}{4-4sint} -\frac{1-sint}{4+4sint}

⇒ (1+sint)(4+4sint)−(1−sint)(4−4sint)(4−4sint)(4+4sint)\frac{(1+sint)(4+4sint) - (1-sint)(4-4sint)}{(4-4sint)(4+4sint)}

⇒ 4+4sint+4sint+(4sint)(sint)−4+4sint+4sint−(4sint)(sint)16[1−(sint)(sint)]\frac{4+4sint+4sint+(4sint)(sint) - 4+4sint+4sint - (4sint)(sint)}{16[1-(sint)(sint)]}

⇒ 16sint16(cost)(cost)\frac{16sint}{16(cost)(cost)}

⇒ tant. sect