0 mehakNewbie Asked: June 24, 20232023-06-24T21:53:08+05:30 2023-06-24T21:53:08+05:30In: CBSE 9. If tan θ = a/b, find the value of (cos θ + sin θ)/ (cos θ – sin θ) 0 Explain the method used. Class 10th, Rd sharma Trigonometric identities. rd sharma class 10thtrigonometric identities Share Facebook 2 Answers Voted Oldest Recent mehak Newbie 2023-06-25T19:51:33+05:30Added an answer on June 25, 2023 at 7:51 pm Solution: Given, 3cot A = 4 ⇒ cot A = 4/3 By definition, tan A = 1/ Cot A = 1/ (4/3) ⇒ tan A = 3/4 Thus, Base side adjacent to ∠A = 4 Perpendicular side opposite to ∠A = 3 In ΔABC, Hypotenuse is unknown. Thus, by applying Pythagoras theorem in ΔABC, We get AC^{2 }= AB^{2} + BC^{2} AC^{2} = 4^{2} + 3^{2} AC^{2} = 16 + 9 AC^{2} = 25 AC = √25 AC = 5 Hence, hypotenuse = 5 Now, we can find that sin A = opposite side to ∠A/ Hypotenuse = 3/5 And, cos A = adjacent side to ∠A/ Hypotenuse = 4/5 Taking the LHS, Thus, LHS = 7/25 Now, taking RHS, 0 Reply Share Share Share on Facebook Share on Twitter Share on LinkedIn Share on WhatsApp mehak Newbie 2023-06-25T19:52:38+05:30Added an answer on June 25, 2023 at 7:52 pm Solution: Given, tan θ = a/b And we know by definition that tan θ = opposite side/ adjacent side Thus, by comparison, Opposite side = a and adjacent side = b To find the hypotenuse, we know that by Pythagoras theorem that Hypotenuse^{2} = opposite side^{2} + adjacent side^{2} ⇒ Hypotenuse = √(a^{2} + b^{2}) So, by definition sin θ = opposite side/ Hypotenuse sin θ = a/ √(a^{2} + b^{2}) And, cos θ = adjacent side/ Hypotenuse cos θ = b/ √(a^{2} + b^{2}) Now, After substituting for cos θ and sin θ, we have ∴ 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 16. A copper sphere of radius 3 cm is melted and recast into a right circular cone of ... 17. A copper rod of diameter 1 cm and length 8 cm is drawn into a wire of ... 18. The diameters of the internal and external surfaces of a hollow spherical shell are 10cm and 6 ... 19. How many coins 1.75 cm in diameter and 2 mm thick must be melted to form a ... 20. The surface area of a solid metallic sphere is 616 cm2. It is melted and recast into ...

Solution:Given,

3cot A = 4

⇒ cot A = 4/3

By definition,

tan A = 1/ Cot A = 1/ (4/3)

⇒ tan A = 3/4

Thus,

Base side adjacent to ∠A = 4

Perpendicular side opposite to ∠A = 3

In ΔABC, Hypotenuse is unknown.

Thus, by applying Pythagoras theorem in ΔABC,

We get

AC

^{2 }= AB^{2}+ BC^{2}AC

^{2}= 4^{2}+ 3^{2}AC

^{2}= 16 + 9AC

^{2}= 25AC = √25

AC = 5

Hence, hypotenuse = 5

Now, we can find that

sin A = opposite side to ∠A/ Hypotenuse = 3/5

And,

cos A = adjacent side to ∠A/ Hypotenuse = 4/5

Taking the LHS,

Thus, LHS = 7/25

Now, taking RHS,

Solution:Given,

tan θ = a/b

And we know by definition that

tan θ = opposite side/ adjacent side

Thus, by comparison,

Opposite side = a and adjacent side = b

To find the hypotenuse, we know that by Pythagoras theorem that

Hypotenuse

^{2}= opposite side^{2}+ adjacent side^{2}⇒ Hypotenuse = √(a

^{2}+ b^{2})So, by definition

sin θ = opposite side/ Hypotenuse

sin θ = a/ √(a

^{2}+ b^{2})And,

cos θ = adjacent side/ Hypotenuse

cos θ = b/ √(a

^{2}+ b^{2})Now,

After substituting for cos θ and sin θ, we have

∴

Hence, proved.