If sec 4A = cosec (A-20°),where 4A is an acute angle , find the value of Aa)12°b)22°c)62°d)82°Correct answer is option 'B'. Can you explain this answer?

Question

If sec 4A = cosec (A-20&deg;),where 4A is an acute angle , find the value of Aa)12&deg;b)22&deg;c)62&deg;d)82&deg;Correct answer is option 'B'. Can you explain this answer?

Answer

Answer

Sec 4A = cosec (A-20)

cosec( 90-4A) = cosec (A- 20)

90-4A = A-20

90+20 = 4A+A

110 = 5A

A = 22

Answer

We know sec and cosec r complementary angles soo... cosec(90-4A)=cosec(A-20) 90-4A=A-20 90+20=A+4A 110=5A A=110/5 A=22  value of A=22

Answer

To find the relationship between sec 4A and cosec(A-20), we need to use trigonometric identities.

Recall the following identities:
1. sec A = 1/cos A
2. cosec A = 1/sin A

Using the first identity, we can rewrite sec 4A as:
sec 4A = 1/cos 4A

Using the second identity, we can rewrite cosec (A-20) as:
cosec (A-20) = 1/sin (A-20)

Now, we need to find a relationship between cos 4A and sin (A-20). To do this, we can use the following identity:
sin (A - B) = sin A * cos B - cos A * sin B

Let's substitute B = 20 into the identity:
sin (A - 20) = sin A * cos 20 - cos A * sin 20

Now, we have a relationship between sin (A-20) and cos 20, sin 20, cos A, and sin A.

Substituting this relationship into cosec (A-20), we get:
cosec (A-20) = 1/(sin A * cos 20 - cos A * sin 20)

Therefore, the relationship between sec 4A and cosec (A-20) is:
sec 4A = 1/cos 4A
cosec (A-20) = 1/(sin A * cos 20 - cos A * sin 20)

Answer

Hmm ok we know that sec and cosec are complementary to each other means sec(90-A)=cosecA, using thud in the given ques we can write it as cosec (90-4A) = cosec(A-20) now, removing cosec from both sides we get 90-4A=A-20 , on solving this or transporting we get = (-5A)=(-110) hence A=110/5 whic is equal to 22

Answer

Answer

Answer

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