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Class 10 math (India)
Course: Class 10 math (India) > Unit 8
Lesson 5: Trigonometric identities- Intro to Pythagorean trigonometric identities
- Converting between trigonometric ratios example: write all ratios in terms of sine
- Evaluating expressions using basic trigonometric identities
- Trigonometric identity example proof involving sec, sin, and cos
- Trigonometric identity example proof involving sin, cos, and tan
- Trigonometric identity example proof involving all the six ratios
- Trigonometric identities challenge problems
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Trigonometric identity example proof involving sec, sin, and cos
Let's try to prove a trigonometric identity involving Secant, sine, and cosine of an angle to understand how to think about proofs in trigonometry. There are many ways to prove these identities. Created by Aanand Srinivas.
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- How would you solve "1- [cos x squared/1 +sin x]?(6 votes)
- I think this is a late answer, but anyway, here you are:
1- [cosX squared/1 +sinX]
= [1 + sinX - (cosX)^2]/1 + sinX
This is possible because 1 = (1 + sinX)/(1 + sinX)
We also know that 1 - (cosX)^2 = (sinX)^2
Now,
[1 - (cosX)^2 + sinX]/1 + sinX
= [(sinX)^2 + sinX]/1 + sinX
Factoring out the sinX,
[sinX (sinX + 1)]/1 + sinX
= [sinX (1 + sinX)]/1 + sinX
= sinX
Hope this helped!(5 votes)
- I got lost for a brief moment, how did you turn that 1 on the right side into 1^2. Do I have to do anything to the equation to achieve that? Or can I write as 1^2 just because I want to?(2 votes)
- Good question!
No, you don't have to do anything to the equation to achieve that, since 1 is equal to 1 squared.
The only reason it is written like that in the video is to portray the a^2 - b^2 format, which can be simplified into (a + b)(a - b), as was done.
Hope this helped!(3 votes)
- Hey,I don't understand this part 1+1/cos A/ 1/cos A part
What did they do in this part(3 votes) - How would you solve (sinx+cosx)^2+(sinx-cosx)^2(2 votes)
- How would you solve
1+sinx/1+cscx = Tanx/secx(2 votes)