What is the value of {sin52^\circ} /{cos38^\circ} + 2tan12^\circ tan32^\circ tan45^\circ tan58^\circ tan78^\circ – 4(\sin^2 35^\circ + \sin^2 55^\circ )?

SSC CPO SI and ASI Model Paper 10

Question : 145 of 200

Marks: +1, -0

What is the value of

{sin52°} /{cos38°} + 2tan12° tan32° tan45° tan58° tan78° – 4(sin^2 35° + sin^2 55° )?

Solution:

(3)

{sin52°}/{cos38°}+ 2tan12 °tan32° tan45° tan58° tan78°– 4(sin^2 35°+ sin^2 55°)

= {sin52°}/{cos (90° – 52°)}+ 2tan12°tan32°tan45°tan(90°– 32°)tan(90°– 12°) – 4(sin^2 35°+sin2(90°- 35°))

= {sin52°}/{sin 52°}+ 2tan12° tan32°tan45° cot32° cot12°– 4(sin^2 35°+cos^2 35°)

= 1 + 2 – 4 = –1

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