If A and B are the angles of a right angled triangle ABC, right angled at C, then 1+cot2A =a)cot2Bb)sec2Bc)cos2Bd)tan2BCorrect answer is option 'B'. Can you explain this answer?

Question

If A and B are the angles of a right angled triangle ABC, right angled at C, then 1+cot2A =&#8203;a)cot2Bb)sec2Bc)cos2Bd)tan2BCorrect answer is option 'B'. Can you explain this answer?

Answer

ABC is a Δ, right angle at c.

1 +cot^2 =?........

we know that.....

Cosec^2 - cot^2= 1...

So,

=> 1+ cot^2

=> cosec^2 A

=> (AB)^2/( CB)^2

= sec ^2B.

Answer

Solution:

We know that, in a right-angled triangle,

cot A = adjacent side/hypotenuse = BC/AB

cot B = adjacent side/hypotenuse = AC/AB

Now, we need to find 1/cot2A.

We know that cot2A = (BC/AB)2 = (cosA/sinA)2 = cos2A/sin2A

So, 1/cot2A = sin2A/cos2A = sec2A

But, we need to express the answer in terms of B, not A.

We know that A + B + 90° = 180° (sum of angles of a triangle)

So, B = 90° - A

Therefore, sec2B = sec2(90° - A) = 1/cos2(90° - A)

We know that cos(90° - A) = sinA

So, cos2(90° - A) = (sinA)2

Therefore, sec2B = 1/(sinA)2 = cosec2A

We also know that cosec2A = 1 + cot2A

So, sec2B = 1 + cot2A

Therefore, 1/cot2A = sec2B - 1 = sec2B [Option B]

Hence, the correct answer is option 'B', i.e. sec2B.

Answer

Answer

The most trigonometric identities are.... cos^2 x+sin^2 x=1 sec^2 x-tan^2 x=1 cosec ^2 x-cot^2 x=1

Answer

Yep convert cot ^2 into cos^2 by sin^2 theta

Answer

1+cot^2A= 1 + cos^2 A /sin^2 A=(sin^2A+cos^a)/sin^2 A=1/sin^A=cosec^A

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