Question-86231

Question Number 86231 by liki last updated on 27/Mar/20

Commented by liki last updated on 27/Mar/20

. . p l z i n e e d h e l p q n n o . 5 (a) & c

Answered by TANMAY PANACEA. last updated on 27/Mar/20

\frac{t a n 145 - t a n 125}{1 + t a n 145 t a n 125}

= t a n (145 - 125)

= t a n 20

= c o t 70

= \frac{1}{t a n 70}

= \frac{1 - {t a n}^{2} 35}{2 t a n 35}

= \frac{1 - x^{2}}{2 x}

Commented by liki last updated on 27/Mar/20

\dots . T h a n k y o u s o m u c h

Answered by TANMAY PANACEA. last updated on 27/Mar/20

c o s x + c o s y = c o s a

s i n x + s i n y = s i n a

a = \frac{7 π}{12} = 105^{o}

f r o m 1) 2 c o s \frac{x + y}{2} c o s \frac{x - y}{2} = c o s a

f r o m 2) 2 s i n \frac{x + y}{2} c o s \frac{x - y}{2} = s i n a

t a n (\frac{x + y}{2}) = t a n a

x + y = 2 a = \frac{7 π}{6} = 210^{o}

4 {c o s}^{2} \frac{x + y}{2} {c o s}^{2} \frac{x - y}{2} + 4 {s i n}^{2} \frac{x + y}{2} {c o s}^{2} \frac{x - y}{2} = 1

4 {c o s}^{2} \frac{x - y}{2} ({c o s}^{2} \frac{x + y}{2} + {s i n}^{2} \frac{x + y}{2}) = 1

c o s \frac{x - y}{2} = \pm \frac{1}{2}

c o s (\frac{x - y}{2}) = \frac{1}{2} = c o s \frac{π}{3}

x - y = 120^{o}

x + y = 210^{o}

2 x = 330^{o} x = 165^{o}

y = 45^{o}

n o w i f

c o s (\frac{x - y}{2}) = \frac{- 1}{2} = c o s 120^{o}

x - y = 240^{o} b u t l o o k

x + y = 210^{o} b u t x - y = 240^{o}

s o c o s (\frac{x - y}{2}) \neq \frac{- 1}{2}

p l s c h e c k \dots

Commented by liki last updated on 27/Mar/20

\dots B e b l e s s e d s i r, i u n d e r s t o o d w e l l!

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