Question

if cos A equal to 7/25,find the value of tan A + cot A

Answer 1

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Answer 2

Cos A = 7 / 25 = Base / Perpendicular

By pythagoras theorem,

Hypotenuse ^2= base ^2 + perpendicular ^2
$cos \: a \: = 7 \div 25 \\ = base \div hypotenuse \\ by \: pythagoras \: theorem \\ hyotenuse {}^{2} = base {}^{2} + perpendicular {}^{2} \\ 25 {}^{2} = 7 {}^{2} + perpendicular {}^{2} \\ perpendicular {}^{2} = 625 - 49 \\ perpendicular {}^{2} = 576 \\ perpendicular = \sqrt{576} = 24$
Cot A = Base / Perpendicular =7/24

Tan A = Perpendicular / Base = 24/7

ATQ,
Tan A + Cot A = 24 /7 + 7 / 24 = 576 + 49 / 168

Tan A + Cot A = 625 /168 = 576. 291667