Blog

Parin Sir > Quantitative Aptitude (Maths) > T-Ratios & Identities > Examples 6 to 10 of T-Ratios & Identities > Examples 6 to 10 of T-Ratios & Identities

Examples 6 to 10 of T-Ratios & Identities

No Comments

 (6) Evaluate :  sin{\frac{\pi}{6}}+cos{\frac{\pi}{3}}-{cot}^3{\frac{\pi}{4}}+cos{e}c^2\frac{\pi}{2}.

Soln. Here,

= sin{\frac{\pi}{6}}+cos{\frac{\pi}{3}}-{cot}^3{\frac{\pi}{4}}+cos{e}c^2\frac{\pi}{2}

=  \frac{1}{2}+\frac{1}{2}-1^3+1^2

=   1

(7) Find the values of :

  (i)   sin 120 o              (ii)   cos 135 o           (iii)   tan ( – 150 o )

 (iv)  cot 300 o              (v)   sec 210 o           (vi)   cosec 420 o

  1. sin 1200 =  sin ( 1800 – 600 )  =  sin 600  =  \frac{\sqrt3}{2}
  2. cos 1350 =  cos ( 1800 – 450 )  =  – cos 45  =  – \frac{1}{\sqrt2}
  3. tan (– 1500 ) = – tan 1500 =  – tan ( 1800– 300)  =   tan 300  =  \frac{1}{\sqrt3}
  4. cot 3000 =  cot ( 2700 + 300 )  =  –  tan 300  =  – \frac{1}{\sqrt3}
  5. sec 2100 =  sec ( 1800 + 300 )  =  – sec 300  =  – \frac{1}{cos{3}0^\circ}  =  – \frac{2}{\sqrt3}
  6. cosec 4200 =  cosec ( 3600 + 600 )  =  cosec 600  =  \frac{1}{sin{6}0^\circ} = \frac{2}{\sqrt3}

 

(8) If  sin θ  =  \frac{1}{2}  and  0 < \theta < 2\pi,  find the values of  θ.

Soln. sin\theta = \frac{1}{2} = sin \frac{\pi}{6}     \large \Rightarrow \theta = k\pi + ( - 1 )k \frac{\pi}{6}

: k \in Z

\Rightarrow \theta = \frac{\pi}{6}

and :  for  k  =  0, 1

0 < \theta < 2\pi

\Rightarrow0 < \theta < \frac{12\pi}{6}

(9) Find  the values of :

(i)  sin 70o – cos 20o          (ii)  sin2 31o + sin2 69o      (iii)  \frac{tan{2}7^o}{cot{6}3^o}

  • sin 700 – cos 200 = sin 700 – cos ( 900 – 700)  =  sin 700 – sin 700  =  0.
  • sin2 310 + sin2 69  =    sin2 310 + sin2 ( 900 – 310 )

=     sin2 310 + cos2 310  =  1.

  • \frac{tan{2}7^o}{cot{6}3^o} =  \frac{tan{(}90^o-63^o)}{cot{6}3^o}= \frac{cot{6}3^o}{cot{6}3^o}  = 1.

 

(10) If  tan 52o  = \frac{a}{b},  find the value of tan 38o.

Soln. tan 380  =  tan ( 900 – 520 )  =  cot 520  =  \frac{b}{a}.

 

Click here to see more examples

Share
educational sutra maths sutr Examples mathematics SUMS ganit example concept math proof Parin theorem sir theorems bhai definition Mehta definitions maheta fundamental classes basic class base education sum online dakhla tutorial formula

Leave a Reply