If A+B=90 then prove that 1+cot²A=sec²B
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★ TRIGONOMETRIC REDUCTIONS ★
Following the given steps in the attachment , resulting expression will yield the identity
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Following the given steps in the attachment , resulting expression will yield the identity
★✩★✩★✩★✩★✩★✩★✩★✩★✩★✩★
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Hey there !
Given ,A+B =90
A=90-B
>> sec²Φ-tan²Φ=1
>> sec²Φ=1+tan²Φ
L.H.S
=1+cot²A
=1+cot²(90-B)
=1+tan²B because sec²Φ-tan²Φ=1
=sec²B
=R.H.S
Hence proved !
Given ,A+B =90
A=90-B
>> sec²Φ-tan²Φ=1
>> sec²Φ=1+tan²Φ
L.H.S
=1+cot²A
=1+cot²(90-B)
=1+tan²B because sec²Φ-tan²Φ=1
=sec²B
=R.H.S
Hence proved !
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