Question

If cos A=7/25 and 3pi/2

Answer 1

CORRECT QUESTION:

If cosA=7/25 and 3π\2 is less than A is less than 2π,value of cotA/2 is?

ANSWER:

COT A/2=-4/3

GIVEN:

cos A = 7/25

3π/2<A<2π

WE KNOW THAT

3π/2 =270° AND 2π =360°

So A will lie in 4th quadrant.In 4th quadrant cot functions Is negative.

WE KNOW THAT,

cot A/2 = cos A/2 / sin A/2

$cos A/2 =\sqrt{\frac{cosA+1}{2}}\\cos A/2=\sqrt{\frac{7/25\:+1}{2}}\\cos A/2=\sqrt{\frac{(7+25)/25}{2}}\\cos A/2=\sqrt{\frac{32}{25}\times\frac{1}{2}}\\cos A/2=\sqrt{\frac{16}{25}}\\cos A/2=\frac{4}{5}$

USING THE BELOW FORMULA,WE CAN GET SinA

sin²A/2 + cos²A/2 = 1

sin²A/2 = $\sqrt{1-cos^2A/2}$

$sin^2 A/2=\sqrt{1-\frac{16}{25}}\\sin^2 A/2=\sqrt{\frac{25-16}{25}}\\sin^2 A/2=\frac{3}{5}\\cotA/2 =\frac{cos A/2}{sin A/2}\\cotA/2 =\frac{\frac{4}{5}}{\frac{3}{5}}\\cotA/2=4/3$

AS A LIES IN THE 4TH QUADRANT COT FUNCTION IS NEGATIVE. HENCE COT A/2=-4/3

Answer 2

cos A/2=√1+cosA /1-cosA

cosA=7/25

√1+7/25by 1-7/25

√(25+7) /25 by (25-7) by 25

√32/18=4/3 theta is negative in 4 th quadrant then cot A/2 =-4/3

HOPE YOU UNDERSTAND