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17 - General Trigonometry Questions Answers

Mathematics >> Trigonometry >> General Trigonometry IIT JEE

(iii) tan69∘+tan66∘+1=tan69∘⋅tan66∘.

Asked By: KHUSHI
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Maths >> Trigonometry >> General Trigonometry Board Exam

Solve

tanx-3cotx=2tan3x(0<x<360)

cosx-sinx=cosy-siny

cos2xcotx+1=cos2x+cotx

Asked By: YUMESH
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Joshi sir comment

tanx - 3/tanx = 2[3tanx-tan3x]/[1-3tan2x]

so [tan2x - 3]/tanx = 2tanx[3-tan2x]/[1-3tan2x]

so [tan2x - 3][1-3tan2x] = 2tan2x[3-tan2x]

so [tan2x - 3][1-3tan2x] + 2tan2x[tan2x-3] = 0

so [tan2x - 3][1-tan2x] = 0

so tanx = 1, -1, √3, -√3

now check the values satisfying last eq.

then put these values in 2nd eq. to get answer.

Maths >> Trigonometry >> General Trigonometry AIEEE

Find the value :-

(tan69 +tan66) / (1 - tan69.tan66)

Asked By: ADARSH
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Joshi sir comment

use formula of tan(A+B)

Maths >> Trigonometry >> General Trigonometry AIEEE

Find the max. and min. value of

y = 7cosA + 24sinA

Asked By: ADARSH
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Joshi sir comment

   7cosA + 24sinA

= 25[7cosA/25 + 24sinA/25] = 25[cosAcosB + sinAsinB]                          where tanB = 24/7

= 25cos[A-B]                    max and min of cos[A-B] = 1 and -1                

so max. = 25  and min. = -25

Maths >> Trigonometry >> General Trigonometry Engineering Exam

Prove that :-

tanA + 2tan2A + 4tan4A + 8cot8A = cosecA / secA

Asked By: ADARSH
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Joshi sir comment

We have to prove

tanA + 2tan2A + 4tan4A + 8cot8A = cosecA / secA

or tanA + 2tan2A + 4tan4A + 8cot8A = cotA

or 2tan2A + 4tan4A + 8cot8A = cotA - tanA

or tan2A + 2tan4A + 4cot8A = [1-tan2A]/2tanA

or tan2A + 2tan4A + 4cot8A = cot2A

or 2tan4A + 4cot8A = cot2A - tan2A

or tan4A + 2cot8A = [1-tan22A]/2tan2A

or tan4A + 2cot8A = cot4A

or 2cot8A = cot4A-tan4A

or cot8A = [1-tan24A]/2tan4A

it is true so proved

Maths >> Trigonometry >> General Trigonometry AIEEE

Prove that :-

sin(A+B+C+D) + sin(A+B-C-D) + sin(A+B-C+D) + sin(A+B+C-D) = 4sin(A+B).cosC.cosD

Asked By: ADARSH
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Joshi sir comment

sin(A+B+C+D) = sin(A+B)[cosCcosD-sinCsinD]+cos(A+B)[sinCcosD+cosCsinD]

similarly solve all the terms and add all these terms for getting answer

Maths >> Trigonometry >> General Trigonometry IIT JEE

((1(secA.secA-cosA.cosA))-(1/(cosecA.cosecA-sinA.sinA))).sinA.sinA.cosA.cosA=(1-cosA.cosA.sinA.sinA)/(2+cosA.cosA.sinA.sinA)

Asked By: VISHVESH CHATURVEDI
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Joshi sir comment

Submit the correct question, In first bracket / will be there so

((1/(secA.secA-cosA.cosA))-(1/(cosecA.cosecA-sinA.sinA))).sinA.sinA.cosA.cosA

= [cos2A/sin2A(1+cos2A) - sin2A/cos2A(1+sin2A)]sin2Acos2A

= [cos4A(1+sin2A) - sin4A(1+cos2A)] / [(1+sin2A)(1+cos2A)]

now solve

 

 

 

 

Maths >> Trigonometry >> General Trigonometry Olympiad

if x is any real number and cosA=x^2+1/2x then cos A value is 

 

Asked By: RAMACHANDRAM
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Joshi sir comment

x2+1 > 2x so cosA>1 which is not possible

Maths >> Trigonometry >> General Trigonometry Board Exam

if x=2Cosθ-Cos2θ and y=2Sinθ-Sin2θ prove that dy/dx=tan(3θ/2)

Asked By: SARABJEET
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Joshi sir comment

calculate dx/dθ and dy/dθ

then dy/dx = [2cosθ-2cos2θ]/[-2sinθ+2sin2θ]

now solve

use cosC-cosD = 2sin[(C+D)/2]sin[(D-C)/2]

and sinC+sinD = 2sin[(C+D)/2]cos[(C-D)/2]

Maths >> Trigonometry >> General Trigonometry Board Exam

What are trigonometrical identities?

Asked By: SIDDHANT KAPOOR
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Joshi sir comment

sin2A + cos2A = 1 and two similar formulae in terms of tanA, cotA, secA and cosecA 

these are identities because these are true for all values of A

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