Question

trigonometric ratio of complementary angle

3 cotton 31 tan 15 cot 27 tan 75 cot 63 cot 59

​

Answer 1

Correct Question:

3cot(31) tan(15) cot(27) tan(75) cot(63) cot(59)

Your Answer:

We know that

cot(90-A) = tan A

tan(90-A) = cot A

So,

cot 31 = cot ( 90 - 59 ) = tan 59

tan 15 = tan ( 90 - 75 ) = cot 75

cot 27 = cot ( 90 - 63 ) = tan 63

Replacing Values in the Equation

= 3 tan 59. cot 75. tan 63.  tan 75. cot 63. cot 59

Taking them in a correct order

= 3 tan 59. cot 59 . cot 75. tan 75. tan 63. cot 63

We also know that cot A. tan A = 1

= 3 (1)(1)(1)

= 3

So, Answer is 3

More to know:

• cos A = sin ( 90 - A )
• sin A = cos ( 90 - A )
• sec A = cosec ( 90 - A )
• cosec A = sec ( 90 - A )
• sin A / cos A = tan A
• cos A / sin A = cot A
• 1/cos A = sec A
• 1/sin A = cosec A

Answer 2

Answer:

3cot(31) tan(15) cot(27) tan(75) cot(63) cot(59)

Your Answer:

We know that

cot(90-A) = tan A

tan(90-A) = cot A

So,

cot 31 = cot ( 90 - 59 ) = tan 59

tan 15 = tan ( 90 - 75 ) = cot 75

cot 27 = cot ( 90 - 63 ) = tan 63

Replacing Values in the Equation

= 3 tan 59. cot 75. tan 63. tan 75. cot 63. cot 59

Taking them in a correct order

= 3 tan 59. cot 59 . cot 75. tan 75. tan 63. cot 63

We also know that cot A. tan A = 1

= 3 (1)(1)(1)

= 3

So, Answer is 3

More to know:

• cos A = sin ( 90 - A )
• sin A = cos ( 90 - A )
• sec A = cosec ( 90 - A )
• cosec A = sec ( 90 - A )
• sin A / cos A = tan A
• cos A / sin A = cot A
• 1/cos A = sec A
• 1/sin A = cosec A