Answer:
Proved that tan45° × sec40° + tan60° × cosec40° =4 by using the trigonometric ratio formulas.
Given that,
We have to prove that tan45° × sec40° + tan60° × cosec40° =4
We know that,
What is trigonometry ratio?
Trigonometric ratios are ratios of triangle side lengths. These ratios in trigonometry demonstrate the relationship between the sides and angles of a right triangle. The three basic ratios in trigonometry are sine, cosine, and tangent.
Take the left hand side
tan45° × sec40° + tan60° × cosec40°
We know that tan45°=1 and tan60°=√3
1×sec40°+√3×cosec40°
sec40°+√3cosec40°
We know that from formula,
sec40° = \frac{1}{cos40\textdegree}
cos40\textdegree
1
and cosec40° = \frac{1}{sin40\textdegree}
sin40\textdegree
1
\frac{1}{cos40\textdegree}
cos40\textdegree
1
+√3× \frac{1}{sin40\textdegree}
sin40\textdegree
1
1+3
4 (Approximately)
Therefore, Proved that tan45° × sec40° + tan60° × cosec40° =4 by using the trigonometric ratio formulas.