Find the value of cos5 -4 cos-4-sin3 -4 cos3 -4

Cos(π + π/4).cos( π/4)/sin(π π/4).cos( π/2 + π/4) = cos π/4× cosπ/4/sin π/4( sin π/4) = cot^2π/4 = (1)^2 = 1 ...

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Standard XI

Mathematics

Basic Trigonometric Identities

Find the valu...

Question

Find the value of $\frac{c o s (\frac{5 π}{4}) c o s (\frac{- π}{4})}{s i n (\frac{3 π}{4}) c o s (\frac{3 π}{4})}$

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Solution

$\frac{c o s (π + \frac{π}{4}) . c o s (- \frac{π}{4})}{s i n (π - \frac{π}{4}) . c o s (\frac{π}{2} + \frac{π}{4})}$

= $\frac{- c o s \frac{π}{4} \times c o s \frac{π}{4}}{s i n \frac{π}{4} (- s i n \frac{π}{4})}$

= $c o t^{2} \frac{π}{4}$

= $(1)^{2}$

= 1

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Find the value of cos(5π4)cos(−π4)sin(3π4)cos(3π4) ___

cos(π+π4).cos(−π4)sin(π−π4).cos(π2+π4) = −cosπ4×cosπ4sinπ4(−sinπ4) = cot2π4 = (1)2 = 1

Find the value of $\frac{c o s (\frac{5 π}{4}) c o s (\frac{- π}{4})}{s i n (\frac{3 π}{4}) c o s (\frac{3 π}{4})}$

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$\frac{c o s (π + \frac{π}{4}) . c o s (- \frac{π}{4})}{s i n (π - \frac{π}{4}) . c o s (\frac{π}{2} + \frac{π}{4})}$

= $\frac{- c o s \frac{π}{4} \times c o s \frac{π}{4}}{s i n \frac{π}{4} (- s i n \frac{π}{4})}$

= $c o t^{2} \frac{π}{4}$

= $(1)^{2}$

= 1