SSC CGL 2024 PYQ — Question 67

The correct answer is Option 1 i.e. 0.

${sec\ 35°\over cosec\ 55°}\ -\ {cos\ 25°\over sin\ 65°}$

⇒ sec 35^∘ = 1/cos35^∘

⇒ cosec 55^∘ = 1/sin 55^∘

Now, 

Solving ${sec\ 35°\over cosec\ 55°}$

⇒ ${{1\over cos35°}\over {1 \over sin55}}$ = ${{sin55\over cos35°} }$ 

Since sin⁡55^∘ = cos⁡35^∘ (because 55^∘ and 35^∘ are complementary angles)

⇒ ${{sin55\over cos35°} }$ = 1

Now, Solving ${cos\ 25°\over sin\ 65°}$

Since 25^∘ and 65^∘ are also complementary angles,

⇒ ${cos\ 25°\over sin\ 65°}$ = ${cos\ 25°\over cos\ 25°}$ = 1

Now,

The value of ${sec\ 35°\over cosec\ 55°}\ -\ {cos\ 25°\over sin\ 65°}$

⇒ 1 - 1 = 0