Question

Sin thita divided by 1- cot thita + cos thita divided by 1- tan thita is equal to sin thita + cos thita prove this​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

using a instead of theta

(sin a/1-cot a)+(cos a/1-tan a)

={sin a/(1-(cos a/sin a)} + {cos a/(1-(sin a/cos a)}.

[Breaking up cot a and tan a]

={sin a/((sin a-cos a)/sin a)} + {cos a/((cos a - sin a)/cos a)}

[taking the LCM]

={sin²a/(sin a-cos)} + {cos²a/(cos a-sin a)}

={sin²a/(sin a-cos)} - {cos²a/(sin a-cos a)}

[ taking - common to make both the LCM equal]

=(sin²a - cos²a)/(sin a-cos a)

={(sin a+cos a)(sin a-cos a)}/(sin a-cos a)

[breaking up sin²a- cos²a]

=sin a+cos a

[ cancelling sin a-cos a both in numerator & denominator]

Hence proved