Question

(cos2 25 + cos2 65) + cosecA sec (90-A) -cotA tan(90-A)

Answer 1

Reason
cos (90-x) = sin x
sec (90-x) =. cosec x
tan (90-x) =. cot x

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Answer 2

Answer : 2

Solution :

${ \cos }^{2} 25 + { \cos }^{2} 65 + \csc \alpha \sec(90 - \alpha ) - \cot\alpha \tan(90 - \alpha ) \\ \\ = > { \cos }^{2} 25 + {( \cos(90 - 25) )}^{2} + \csc\alpha . \csc \alpha - \cot \alpha . \cot \alpha \\ \\ As \: we \: know \: that: \: \sec(9 0 - \alpha ) = \csc\alpha \: and \: \tan(90 - \alpha ) = \cot\alpha \\ \\ also \: \cos(90 - \alpha ) = \sin \alpha \\ \\ = > { \cos }^{2} 25 + { \sin}^{2} 25 + { \csc }^{2} \alpha - { \cot }^{2} \alpha \\ \\ = > 1 + 1 \\ \\ ( { \sin }^{2} \alpha + { \cos}^{2} \alpha = 1 \: and \: { \csc}^{2} \alpha = 1 + { \cot }^{2} \alpha ) \\ \\ = > 2$