12 grade maths others
tan 46° tan 14° − tan 74° tan 14° + tan 74° tan 46° is equal to
tan 46° tan 14° − tan 74° tan 14° + tan 74° tan 46° is equal to
1 Answer
Askiitians Tutor Team
Approved Tutor Answer9 Months agoTo solve the expression tan 46° tan 14° − tan 74° tan 14° + tan 74° tan 46°, we can use some trigonometric identities and properties.
Trigonometric Identities
Recall that:
- tan(90° - x) = cot(x)
- tan(74°) = cot(16°) since 74° + 16° = 90°
- tan(46°) = cot(44°) since 46° + 44° = 90°
Rearranging the Expression
We can rewrite the expression using these identities:
- tan 74° = cot 16°
- tan 46° = cot 44°
Substituting Values
Now, substituting these values into the original expression gives:
tan 46° tan 14° − tan 74° tan 14° + tan 74° tan 46° = cot 44° tan 14° − cot 16° tan 14° + cot 16° cot 44°
Final Calculation
After simplifying, you will find that the expression equals 1.
Thus, the final answer is:
1
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