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Question and Answer

\( tan35°. tan40°.tan45°.tan50°tan55° \) is equal to
(A) 1
(B) 2
(C) 0
(D) 3

Answer

(A)
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Solution

\( tan35°.tan40°.tan45°tan50°tan55° \)
\( =tan\left(90°-55°\right)tan\left(90°-50°\right)tan45°tan50°.tan55°  \)
\( \therefore\;tan\left(90°-\theta \right)=cot\theta ) \)
\( =cot55°cot50°\times\;1\times\;tan50°tan55°\)
\( =\frac{1}{tan55°} \frac{1}{tan50°}tan50°tan55° \)
= 1
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