Question

Which of following formula is true :
(a) Cos²0 - Sin²0=1
(b) Cos 20=1 - Sin²o
(c) Cos 20=2 Sino Cos0
(d) Sin 20=2Sino Cos0​

Answer 1

Answer:

Step-by-step explanation:

Option b

Sin^20+cos^20=1

Cos^20=1-sin^20

This is correct answer

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Answer 2

Correct formula is given in option d.

$\bf {sin}2 \: \theta = 2{sin} \theta \: cos\theta$

Given:

• $(a) \: {cos}^{2} \theta - {sin}^{2} \theta = 1$
• $( b) \: {cos}2 \theta = 1 - {sin}^{2} \theta$
• $( c) \: {cos}2 \theta = 2{sin} \theta \: cos\theta$
• $( d) \: {sin} \: 2 \theta = 2{sin} \theta \: cos\theta$

To find:

• Which of the above written formula is true?

Solution:

$\bf \: {sin} \: 2 \theta = 2{sin} \theta \: cos\theta$

Formula of option (d) is correct/True.

Why rest of the options are not true:

Case 1: Option (a)

${cos}^{2} \theta - {sin}^{2} \theta = 1$

The correct formula for option a is

$\bf {cos}^{2} \theta + {sin}^{2} \theta = 1$

Case 2: Option (b)

${cos}2 \theta = 1 - {sin}^{2} \theta$

The correct formula for option b is

$\bf {cos}2 \theta = 1 - 2{sin}^{2} \theta$

Case 3: Option (c)

${cos}2 \theta = 2{sin} \theta \: cos\theta$

The correct formula for option c is

$\bf {sin}2 \: \theta = 2{sin} \theta \: cos\theta$

Thus,

Correct formula is given in option d.

$\bf {sin}2 \: \theta = 2{sin} \theta \: cos\theta$

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