if 2 sin theeta - 4cos theeta = 0, find tan²theeta + 1 / sec theeta
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Solution
We have,
3 sin 0 + 4cos = 5
. (1)
On squaring both sides, we get
(3 sin 0 + 4cos0)² = 5²
9sin²0+16cos²0 + 24 sin cos
= 25
9 (1 − cos²0) + 16 (1 - sin²0) + 12×
2 sin Ꮎ cos Ꮎ
: 25
99cos²0 +16 - 16sin²0 + 12 x
2 sin cos = 25
259cos²016sin²0 + 12 × 2 sin 0 cos 0 = 25 9cos²0 + 16sin²0 12 x 2 sin 0 cos 0 = 0
(3 cos 0 - 4sin0)² = 0
3 cos - 4sin 0
Hence, the value is 0.
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