Tuesday, October 4, 2022
HomeMathProving Trigonometric Identities Worksheet with Options

Proving Trigonometric Identities Worksheet with Options


(1) Decide whether or not every of the next is an identification or not.

(i) cos2θ + sec2θ  =  2 + sinθ     

(ii) cot2θ + cosθ  =  sin2θ   

Answer

(2) Show the next identities

(i) sec2θ + cosec2θ  =  sec2θcosec2θ        Answer

(ii) sinθ/(1 – cosθ)  =  cosecθ + cotθ       Answer

(iii) (1 – sinθ)/(1 + sinθ)  =  secθ – tanθ    Answer

(iv) cosθ/(secθ – tanθ)  =  1 + sinθ        Answer

(v)
√(sec
2θ + cosec2θ)  =  tanθ + cotθ      Answer

(vi) (1 + cosθ – sin2θ)/(sinθ)(1 + cosθ)  =  cotθ 

Answer

(vii) secθ(1 – sinθ)(secθ + tanθ)  =  1      Answer  

(viii) sinθ/(cosecθ + cotθ)  =  1 – cosθ      Answer

(3) Show the next identities

(i) [sin(90 – θ)/(1 + sinθ)] + [cosθ/(1 – (cos(90 – θ))]

=  2secθ       Answer

(ii) tanθ/(1 – cotθ) + cotθ/(1 – tanθ)  =  1 + secθ cosecθ  

Answer

(iii) sin(90 – θ)/(1 – tanθ) + cos(90 – θ)/(1 – cotθ) 

=  cosθ + sinθ      Answer

(iv) [tan(90 – θ)/(cosecθ + 1)] + [(cosecθ + 1)/cotθ)]

=  2secθ       Answer

(v) (cotθ + cosecθ – 1)/(cotθ – cosecθ + 1) 

=  cosecθ + cotθ    Answer

(vi) (1 + cotθ – cosecθ)(1 + tanθ + secθ)  =  2        Answer

(vii) (sinθ – cosθ + 1)/(sinθ + cosθ – 1)  =  1/(secθ-tanθ) 

Answer

(viii) tanθ/(1 – tan2θ) = sinθsin(90 – θ)/[2sin2(90 – θ) – 1]  

(ix) [1/(cosecθ – cotθ)] – (1/sinθ) 

=  [(1/sinθ)] – [1/(cosecθ + cotθ)]             Answer

(x) (cot2θ  + sec2θ)/(tan2θ + cosec2θ)

=  sinθ cosθ(tanθ + cotθ)        Answer

(4) If x = a sec θ + b tan θ and y = a tan θ + b sec θ then show that

x2 – y2  =  a2 – b2          Answer

Solo Build It!

Kindly mail your suggestions to v4formath@gmail.com

We at all times respect your suggestions.

©All rights reserved. onlinemath4all.com






RELATED ARTICLES

LEAVE A REPLY

Please enter your comment!
Please enter your name here

Most Popular

Recent Comments