Question

sec 25 degree /cosec 65 degree + sin /49 degree / cos 41 degree​

Answer 1

GIVEN :-

TRIGNOMATRIC VALUES :

• $\rm{ \dfrac{sec \: 25}{cosec \: 65} } \: + \dfrac{sin \: 49}{cos \: 41}$

TO FIND :-

WE HAVE TO FIND THE VALUE OF

• $\rm{ \dfrac{sec \: 25}{cosec \: 65} } \: + \dfrac{sin \: 49}{cos \: 41}$

SOLUTION : -

WE KNOW THAT

$\implies \boxed{\rm { sec \: a = cosec \: (90 - a)}}$

hence ,

$\implies \: \rm{ sec \: 25 = cosec \: (90 - 25) \: }$

$\implies \: \rm{ sec \: 25 = cosec \: 65 - - - \: eq \: 1 \: }$

ALSO WE KNOW THAT ,

$\implies \boxed{\rm { sin \: a = cos \: (90 - a)}}$

hence,

$\implies \: \rm{ sec \: 25 = cosec \: (90 - 25) \: }$

$\implies \: \rm{ sin\: 49 = cos\:41 \: - - - \: eq \: 2 }$

NOW BUT EQUATION 1 AND EQUATION 2 IN

$\implies \: \rm{ \dfrac{sec \: 25}{cosec \: 65} } \: + \dfrac{sin \: 49}{cos \: 41}$

$\implies \: \rm{ \dfrac{cosec \: 65}{cosec \: 65} } \: + \dfrac{cos \: 41}{cos \: 41}$

$\implies \: \rm{ 1+ 1 = 2}$

$\implies \boxed {\boxed {\: \rm{ \dfrac{sec \: 25}{cosec \: 65} } \: + \dfrac{sin \: 49}{cos \: 41 } = 2}}$

OTHER INFORMATION :-

TRIGNOMETRIC IDENTITIES :-

• SIN²∅ + COS²∅ = 1

• SEC²∅ - TAN²∅ = 1

• COSEC²∅ - COT²∅ = 1

TRIGNOMETRIC COMPLEMENTARY ANGLES :-

• SIN 90 = COS ( 90 - ∅ )

• COS 90 = SIN ( 90 - ∅ )

• TAN 90 = COT ( 90 - ∅ )

• COT 90 = TAN ( 90 - ∅ )

• COSEC 90 = SEC ( 90 - ∅ )

• SEC 90 = COSEC ( 90 - ∅ )

TRIGNOMATERIC RATIOS :-

• SIN ∅ = 1/ COSEC ∅

• COS ∅ = 1/ SEC ∅

• TAN ∅ = 1/ COT ∅

• TAN ∅ = SIN ∅ / COS ∅

• COT ∅ = COS ∅ / SIN ∅