Prove that 2 sin &#x2061;<!-- ⁡ --> ( a ) +

Nylah Hendrix

Nylah Hendrix

Answered question

2022-07-03

Prove that 2 sin ( a ) + sec ( a ) 1 + tan ( a )

Answer & Explanation

Tamia Padilla

Tamia Padilla

Beginner2022-07-04Added 16 answers

Although no method is foolproof, I've had few problems with this one.
Step 1: Take what you started with and multiply by 1.
2 sin a + sec a 1 + tan a 1
Step 2: Split up 1 into what you want to end up with and its reciprocal.
2 sin a + sec a 1 + tan a ( sec a 1 + tan a 1 + tan a sec a )
Step 3: Group the reciprocal with what you started with.
( 2 sin a + sec a 1 + tan a sec a 1 + tan a ) 1 + tan a sec a
Step 4: Show that what is in parentheses is equal to 1.
= ( 2 sin a sec a + sec 2 a ( 1 + tan a ) 2 ) 1 + tan a sec a
= ( 2 tan a + ( tan 2 a + 1 ) ( 1 + tan a ) 2 ) 1 + tan a sec a
= ( tan 2 a + 2 tan a + 1 ( 1 + tan a ) 2 ) 1 + tan a sec a
= ( ( 1 + tan a ) 2 ( 1 + tan a ) 2 ) 1 + tan a sec a
= 1 1 + tan a sec a = 1 + tan a sec a

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