A student hands in this four-step "proof" that sin A + cos A = 1: Step 1: ^2 A + ^2 A = 1 Step 2: ^2 A = 1 - ^2 A Step 3: A = 1 - A Step 4: A + A = 1 Which is the FIRST step that is wrong?

Question

Accepted Answer

Step 3. Steps 1 and 2 are correct. Step 3 takes a square root term by term: from ^2 A = 1 - ^2 A you may only write A = √1 - ^2 A , and √1 - ^2 A is NOT 1 - A . Check at A = 30°: 30^° = 0.5 while 1 - 30^° 0.134 . Step 4 merely repeats the error already made in Step 3.

A student hands in this four-step "proof" that sin A + cos $A = 1$ :
Step 1: $sin^{2} A + cos^{2} A = 1$
Step 2: $sin^{2} A = 1 - cos^{2} A$
Step 3: $sin A = 1 - cos A$
Step 4: $sin A + cos A = 1$
Which is the FIRST step that is wrong?

Step-by-Step Solution

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More Class 10 Trigonometric Identities practice

A student hands in this four-step "proof" that sin A + cos A=1:Step 1: sin2A+cos2A=1Step 2: sin2A=1−cos2AStep 3: sinA=1−cosAStep 4: sinA+cosA=1Which is the FIRST step that is wrong?

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Trigonometric Identities practice

A student hands in this four-step "proof" that sin A + cos $A = 1$ :
Step 1: $sin^{2} A + cos^{2} A = 1$
Step 2: $sin^{2} A = 1 - cos^{2} A$
Step 3: $sin A = 1 - cos A$
Step 4: $sin A + cos A = 1$
Which is the FIRST step that is wrong?