Question

(sinA + coseca) 2+ (cosa+seca)2=7tan2a+cot2a​

Answer 1

Concept :

In a right angled triangle, the cosine of an angle is:

• The length of the adjacent side divided by the length of the hypotenuse.

• The abbreviation is cos.

• cos(θ) = adjacent / hypotenuse.

Let's start :

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf⇝L.H.S =(sinA + cosecA)²+(cosA + secA)²$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf⇝Sin² A + Cosec²A +2 sinA cosecA + co²A + sec²A +2cosA secA$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf⇝1 + 2+ 2+ 1+ tan²A + 1+cot²A$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf⇝7+tan²A+cot² A = R.H.S$

$\underline{ \boxed{ \sf{ \purple{∴1+cot² A= cosec² A \: and \: 1+tan²A = Sec²A}}}}$

Other information :

• In mathematics, the sine is a trigonometric function of an angle.

• The sine of an acute angle is defined in the context of a right triangle.

• For the specified angle, it is the ratio of the length of the side that is opposite that angle, to the length of the longest side of the triangle (the hypotenuse).

Signs :

• Sine and cosine — a.k.a., sin(θ) and cos(θ) — are functions revealing the shape of a right triangle.

• Looking out from a vertex with angle θ, sin(θ) is the ratio of the opposite side to the hypotenuse , while cos(θ) is the ratio of the adjacent side to the hypotenuse