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Question
tan 100° + tan 125° + tan 100° tan 125° = ______.
Options
0
`1/2`
– 1
1
MCQ
Fill in the Blanks
Solution
tan 100° + tan 125° + tan 100° tan 125° = 1.
Explanation:
tan(100° + 125°) = `(tan 100^circ + tan 125^circ)/(1 - tan 100^circ tan 125^circ)`
∴ tan 225° = `(tan 100^circ + tan 125^circ)/(1 - tan 100^circ tan 125^circ)`
i.e. 1 = `(tan 100^circ + tan 125^circ)/(1 - tan 100^circ tan 125^circ)`
i.e. tan 100° + tan 125° + tan 100° tan 125° = 1
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Trigonometric Functions of Sum and Difference of Angles
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