Find the value of θ (0° < θ < 90°) if:
(i) cos 63° sec (90° – θ) = 1
(ii) tan 35° cot (90° – θ) = 1.
Answer :
(i) cos 63° sec (90° – θ) = 1
cos 63° = 1/sec(90° – θ)
1/sec θ = cos θ
cos 63° = cos (90° – θ)
90° – θ = 63°
θ = 90° – 63° = 27°
(ii) tan 35° cot (90° – θ) = 1
tan 35° = 1/cot (90° – θ)
1/cot θ = cos θ
tan 35° = tan (90° – θ)
35° = 90° – θ
θ = 90° – 35°
= 55°
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