# if sinx+sin2x=2then find,cos2x+cos4x

Vinay Arya
37 Points
13 years ago

Hi Vishwa Sharma

sinx+sin2x=2

=>sinx+sin2x-2=0

=>(sinx-1)(sinx+2)=0

=>sinx=1 or sinx=-2

We know that sinx cannot be equal to -2.Hence rejaecting sinx=-2

Therefore, sinx=1 =>x=pi/2

cos2x+cos4x=xos2pi/2 + cos4pi/2 =0

Chaitanya Borah
34 Points
13 years ago

sinx+sin2x=2

=>sinx=1+1-sin2x

=>sinx=1+cos2x

=>cos2x=sinx-1

now,

cos2x+cos4x

=cos2x+(sinx-1)2

=cos2x+sin2x-2sinx+1

=1-2sinx+1

=2(1-sinx)
The text passage contains a mathematical question and multiple answers provided by different users. The question is about finding the value of cos2x + cos4x given a specific trigonometric equation.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# if sinx+sin2x=2then find,cos2x+cos4x

Vinay Arya
37 Points
13 years ago

Hi Vishwa Sharma

sinx+sin2x=2

=>sinx+sin2x-2=0

=>(sinx-1)(sinx+2)=0

=>sinx=1 or sinx=-2

We know that sinx cannot be equal to -2.Hence rejaecting sinx=-2

Therefore, sinx=1 =>x=pi/2

cos2x+cos4x=xos2pi/2 + cos4pi/2 =0

Chaitanya Borah
34 Points
13 years ago

sinx+sin2x=2

=>sinx=1+1-sin2x

=>sinx=1+cos2x

=>cos2x=sinx-1

now,

cos2x+cos4x

=cos2x+(sinx-1)2

=cos2x+sin2x-2sinx+1

=1-2sinx+1

=2(1-sinx)
user
The text passage contains a mathematical question and multiple answers provided by different users. The question is about finding the value of cos2x + cos4x given a specific trigonometric equation.

TYPE: SINGLE_QUESTION_WITH_ANSWER