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Question

If tanα=kcotβ, then cosα-βcosα+β is equal to


A

1+k1-k

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B

1-k1+k

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C

k+1k-1

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D

k-1k+1

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Solution

The correct option is A

1+k1-k


Explanation for the correct option:

Step 1: Given that,

tanα=kcotβtanαcotβ=ksinαcosαsinβcosβ=kk=sinαsinβcosαcosβ...1

Step 2: Apply the formula

=cosα-βcosα+βcosa+b=cosacosb-sinasinbandcosa-b=cosacosb+sinasinb

=cosαcosβ+sinαsinβcosαcosβ-sinαsinβ

Step 3: On dividing numerator & denominator by cosαcosβ

cosα-βcosα+β=cosαcosβ+sinαsinβcosαcosβcosαcosβ-sinαsinβcosαcosβ=1+sinαsinβcosαcosβ1-sinαsinβcosαcosβ

Step 4: From the equation 1

cosα-βcosα+β=1+k1-k

Hence, the correct option is (A).


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