0 Rajan@2021Guru Asked: April 4, 20212021-04-04T18:03:14+05:30 2021-04-04T18:03:14+05:30In: CBSE If tanθ=4/3, show that (sinθ+cosθ)=7/5 0 This is the basic and conceptual question from trigonometric ratios in which we have given that if tanθ=4/3, we have been asked to show that (sinθ+cosθ)=7/5. RS Aggarwal, Class 10, Chapter 10, question no 18. class 10 cbsers aggarwaltrigonometry Share Facebook 1 Answer Voted Oldest Recent MathsMentor Guru 2021-04-05T15:42:00+05:30Added an answer on April 5, 2021 at 3:42 pm Given, tanθ=4/3. cotθ=1/(4/3)=3/4 [ Since, 1/tanθ=cotθ ] We know that, tanθ= opposite side to theta / adjacent side to theta. So, opposite side =4 , Adjacent side =3 Hypotenuse = (4²+3²)=5 Now, sinθ= Opposite side to theta / Hypotenuse =4/5 cosθ= Adjacent side to theta / Hypotenuse =3/5 To prove : sinθ+cosθ=7/5. L. H.S =sinθ+cosθ =4/5+3/5 =7/5 = R. H. S Hence proved! 0 Reply Share Share Share on Facebook Share on Twitter Share on LinkedIn Share on WhatsApp Leave an answerLeave an answerCancel reply Featured image Select file Browse Add a Video to describe the problem better. Video type Youtube Vimeo Dailymotion Facebook Choose from here the video type. Video ID Put Video ID here: https://www.youtube.com/watch?v=sdUUx5FdySs Ex: "sdUUx5FdySs". Click on image to update the captcha. Save my name, email, and website in this browser for the next time I comment. Related Questions Solve the following quadratic equation: √2x²+7x+5√2=0. Solve the following quadratic equation: x²+3√3x-30=0 Solve the following quadratic equation: x²-(√3-1)x+√3=0 Solve the following quadratic equation: x²-3√5x+10=0 Solve the following quadratic equation: √3x²-2√2x-2√3=0

Given,

tanθ=4/3.

cotθ=1/(4/3)=3/4

[ Since, 1/tanθ=cotθ ]

We know that,

tanθ= opposite side to theta / adjacent side to theta.

So, opposite side =4 , Adjacent side =3

Hypotenuse = (4²+3²)=5

Now,

sinθ= Opposite side to theta / Hypotenuse =4/5

cosθ= Adjacent side to theta / Hypotenuse =3/5

To prove : sinθ+cosθ=7/5.

L. H.S

=sinθ+cosθ

=4/5+3/5

=7/5

= R. H. S

Hence proved!